diff --git a/html/ode_extras/01-ModelingToolkit.html b/html/ode_extras/01-ModelingToolkit.html index 8cacdb18..5af8854a 100644 --- a/html/ode_extras/01-ModelingToolkit.html +++ b/html/ode_extras/01-ModelingToolkit.html @@ -698,7 +698,7 @@

Basic usage: defining differential equation systems, with performance! - +

ModelingToolkit is a compiler for mathematical systems

At its core, ModelingToolkit is a compiler. It's IR is its type system, and its output are Julia functions (it's a compiler for Julia code to Julia code, written in Julia).

@@ -1410,6 +1410,7 @@

Hackability: Extend directly from the language

Status `/builds/JuliaGPU/DiffEqTutorials.jl/tutorials/ode_extras/Project.toml`
 [f3b72e0c-5b89-59e1-b016-84e28bfd966d] DiffEqDevTools 2.22.0
+[0c46a032-eb83-5123-abaf-570d42b7fbaa] DifferentialEquations 6.14.0
 [961ee093-0014-501f-94e3-6117800e7a78] ModelingToolkit 3.11.0
 [76087f3c-5699-56af-9a33-bf431cd00edd] NLopt 0.6.0
 [2774e3e8-f4cf-5e23-947b-6d7e65073b56] NLsolve 4.4.0
diff --git a/html/ode_extras/02-feagin.html b/html/ode_extras/02-feagin.html
index 65aeb3f2..df0f221b 100644
--- a/html/ode_extras/02-feagin.html
+++ b/html/ode_extras/02-feagin.html
@@ -668,52 +668,73 @@ 
Investigation of the Method's Error

 
 
 
-using DifferentialEquations
-

-
-
-
-ERROR: ArgumentError: Package DifferentialEquations not found in current path:
-- Run `import Pkg; Pkg.add("DifferentialEquations")` to install the DifferentialEquations package.
-
-

-
-
-
-
-const linear_bigα = big(1.01)
+using DifferentialEquations
+const linear_bigα = big(1.01)
 f(u,p,t) = (linear_bigα*u)
 
 # Add analytical solution so that errors are checked
 f_analytic(u0,p,t) = u0*exp(linear_bigα*t)
-ff = ODEFunction(f,analytic=f_analytic)
-

-
-
-
-ERROR: UndefVarError: ODEFunction not defined
-

-
-
-
-
-prob = ODEProblem(ff,big(0.5),(0.0,1.0))
-

-
-
-
-ERROR: UndefVarError: ODEProblem not defined
+ff = ODEFunction(f,analytic=f_analytic)
+prob = ODEProblem(ff,big(0.5),(0.0,1.0))
+sol = solve(prob,Feagin14(),dt=1//16,adaptive=false);
 

 
 
-
-
-sol = solve(prob,Feagin14(),dt=1//16,adaptive=false);
-

-
-
-
-ERROR: UndefVarError: Feagin14 not defined
+
+retcode: Success
+Interpolation: 3rd order Hermite
+t: 17-element Array{Float64,1}:
+ 0.0
+ 0.0625
+ 0.125
+ 0.1875
+ 0.25
+ 0.3125
+ 0.375
+ 0.4375
+ 0.5
+ 0.5625
+ 0.625
+ 0.6875
+ 0.75
+ 0.8125
+ 0.875
+ 0.9375
+ 1.0
+u: 17-element Array{BigFloat,1}:
+ 0.50
+ 0.532579987953539129415175692266310012757570127936767465729988951844872703
+1384926
+ 0.567282887137183768410176093811331902816684984885556550153431181534165966
+2084392
+ 0.604247026395540457858840348261076470751584579123060668349121048671882781
+8716904
+ 0.643619748077397554810695151333134437286938781958375274884622802079377793
+549762
+ 0.685557995355440557982096349246370736930808950070979750802507189818563351
+642024
+ 0.730228937815705933608434940588601030880998724704814215187999930588230616
+9718902
+ 0.777810637810428680311119693945339493753691675945670302006794689942184819
+812709
+ 0.828492760230425386904283967004764522632796405328715089108453503441096967
+5378266
+ 0.882477328526228669757698486772395431354193449529466082277853631417758596
+1942936
+ 0.939979529991540515340224856861894727292044008413711564360467630700841985
+3257788
+ 1.001228573518936040932179654581424903118245024943528049619445960282439336
+451516
+ 1.066468603246908246544672423846706082660227135054504931710469065776180175
+33485
+ 1.135959671740132190447259472795962527154069506739201242159983984002811333
+382739
+ 1.209978776582131731617034761065124311009358614495571372335128166979326800
+445978
+ 1.288820964512299462579706253102020998553494397009716401282671347081826473
+196884
+ 1.372800507508458259187784036450083092262707343306282981254591926965493411
+372691
 

 
 
@@ -723,8 +744,12 @@ 
Investigation of the Method's Error

 

 
 
-
-ERROR: UndefVarError: sol not defined
+
+Dict{Symbol,BigFloat}(:l∞ => 2.19751040342660991781470263264956056068365936
+7683780324635801610297349872909655e-23,:final => 2.197510403426609917814702
+632649560560683659367683780324635801610297349872909655e-23,:l2 => 1.0615015
+97814768635894514677590712762248364686527596359902826841740549975688161e-23
+)
 

 
 
@@ -745,23 +770,18 @@ 
Investigation of the Method's Error

 
 
 
-sol =solve(prob,Feagin14());
-

-
-
-
-ERROR: UndefVarError: Feagin14 not defined
+sol =solve(prob,Feagin14());
+println(sol.errors); print("The length was $(length(sol))")
 

 
 
-
-
-println(sol.errors); print("The length was $(length(sol))")
-

-
-
-
-ERROR: UndefVarError: sol not defined
+
+Dict{Symbol,BigFloat}(:l∞ => 1.54573888394314096254653759860975921981641479
+0728029220638828884206395861982752e-09,:final => 1.545738883943140962546537
+598609759219816414790728029220638828884206395861982752e-09,:l2 => 8.9250668
+70202330409924421192162193462506388332261074725109949218067763405137993e-10
+)
+The length was 3
 

 
 
@@ -777,8 +797,244 @@ 
Convergence Test

 

 
 
-
-ERROR: UndefVarError: Feagin14 not defined
+
+DiffEqDevTools.ConvergenceSimulation{DiffEqBase.ODESolution{BigFloat,1,Arra
+y{BigFloat,1},Array{BigFloat,1},Dict{Symbol,BigFloat},Array{Float64,1},Arra
+y{Array{BigFloat,1},1},DiffEqBase.ODEProblem{BigFloat,Tuple{Float64,Float64
+},false,DiffEqBase.NullParameters,DiffEqBase.ODEFunction{false,typeof(Main.
+##WeaveSandBox#253.f),LinearAlgebra.UniformScaling{Bool},typeof(Main.##Weav
+eSandBox#253.f_analytic),Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,No
+thing,Nothing,Nothing,Nothing,Nothing},Base.Iterators.Pairs{Union{},Union{}
+,Tuple{},NamedTuple{(),Tuple{}}},DiffEqBase.StandardODEProblem},OrdinaryDif
+fEq.Feagin14,OrdinaryDiffEq.InterpolationData{DiffEqBase.ODEFunction{false,
+typeof(Main.##WeaveSandBox#253.f),LinearAlgebra.UniformScaling{Bool},typeof
+(Main.##WeaveSandBox#253.f_analytic),Nothing,Nothing,Nothing,Nothing,Nothin
+g,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{BigFloat,1},Array{
+Float64,1},Array{Array{BigFloat,1},1},OrdinaryDiffEq.Feagin14ConstantCache{
+BigFloat,Float64}},DiffEqBase.DEStats}}(DiffEqBase.ODESolution{BigFloat,1,A
+rray{BigFloat,1},Array{BigFloat,1},Dict{Symbol,BigFloat},Array{Float64,1},A
+rray{Array{BigFloat,1},1},DiffEqBase.ODEProblem{BigFloat,Tuple{Float64,Floa
+t64},false,DiffEqBase.NullParameters,DiffEqBase.ODEFunction{false,typeof(Ma
+in.##WeaveSandBox#253.f),LinearAlgebra.UniformScaling{Bool},typeof(Main.##W
+eaveSandBox#253.f_analytic),Nothing,Nothing,Nothing,Nothing,Nothing,Nothing
+,Nothing,Nothing,Nothing,Nothing,Nothing},Base.Iterators.Pairs{Union{},Unio
+n{},Tuple{},NamedTuple{(),Tuple{}}},DiffEqBase.StandardODEProblem},Ordinary
+DiffEq.Feagin14,OrdinaryDiffEq.InterpolationData{DiffEqBase.ODEFunction{fal
+se,typeof(Main.##WeaveSandBox#253.f),LinearAlgebra.UniformScaling{Bool},typ
+eof(Main.##WeaveSandBox#253.f_analytic),Nothing,Nothing,Nothing,Nothing,Not
+hing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{BigFloat,1},Arr
+ay{Float64,1},Array{Array{BigFloat,1},1},OrdinaryDiffEq.Feagin14ConstantCac
+he{BigFloat,Float64}},DiffEqBase.DEStats}[retcode: Success
+Interpolation: 3rd order Hermite
+t: [0.0, 0.0009765625, 0.001953125, 0.0029296875, 0.00390625, 0.0048828125,
+ 0.005859375, 0.0068359375, 0.0078125, 0.0087890625  …  0.9912109375, 0.992
+1875, 0.9931640625, 0.994140625, 0.9951171875, 0.99609375, 0.9970703125, 0.
+998046875, 0.9990234375, 1.0]
+u: BigFloat[0.50, 0.5004934073532741442240167407783486492180603021615841294
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+, 1.37280050750845825918780601155411735836188549033294491231479506286094526
+5969766], retcode: Success
+Interpolation: 3rd order Hermite
+t: [0.0, 0.001953125, 0.00390625, 0.005859375, 0.0078125, 0.009765625, 0.01
+171875, 0.013671875, 0.015625, 0.017578125  …  0.982421875, 0.984375, 0.986
+328125, 0.98828125, 0.990234375, 0.9921875, 0.994140625, 0.99609375, 0.9980
+46875, 1.0]
+u: BigFloat[0.50, 0.5009873016081808184403552812231889505849105976869970947
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+372800507508458259187806011554117358361885495412387216596637263939057644809
+585], retcode: Success
+Interpolation: 3rd order Hermite
+t: [0.0, 0.00390625, 0.0078125, 0.01171875, 0.015625, 0.01953125, 0.0234375
+, 0.02734375, 0.03125, 0.03515625  …  0.96484375, 0.96875, 0.97265625, 0.97
+65625, 0.98046875, 0.984375, 0.98828125, 0.9921875, 0.99609375, 1.0]
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+66, 1.372800507508458259187806011554117358361955140865683163444664161725836
+562110807], retcode: Success
+Interpolation: 3rd order Hermite
+t: [0.0, 0.0078125, 0.015625, 0.0234375, 0.03125, 0.0390625, 0.046875, 0.05
+46875, 0.0625, 0.0703125  …  0.9296875, 0.9375, 0.9453125, 0.953125, 0.9609
+375, 0.96875, 0.9765625, 0.984375, 0.9921875, 1.0]
+u: BigFloat[0.50, 0.5039609190120951874615456397052524112111879130152678185
+972878772909801438539725, 0.50795321578303112915468385810466743883495202114
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+4, 1.3728005075084582591878060115541173590617414861285190771349018784370260
+32283726], retcode: Success
+Interpolation: 3rd order Hermite
+t: [0.0, 0.015625, 0.03125, 0.046875, 0.0625, 0.078125, 0.09375, 0.109375, 
+0.125, 0.140625  …  0.859375, 0.875, 0.890625, 0.90625, 0.921875, 0.9375, 0
+.953125, 0.96875, 0.984375, 1.0]
+u: BigFloat[0.50, 0.5079532157830311291546838581046674228648435931525498190
+278213939882467623443407, 0.51603293884864516922308309058199688204679557555
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+27, 1.372800507508458259187806011554114596757211232433432893362855858032659
+14211007], retcode: Success
+Interpolation: 3rd order Hermite
+t: [0.0, 0.03125, 0.0625, 0.09375, 0.125, 0.15625, 0.1875, 0.21875, 0.25, 0
+.28125  …  0.71875, 0.75, 0.78125, 0.8125, 0.84375, 0.875, 0.90625, 0.9375,
+ 0.96875, 1.0]
+u: BigFloat[0.50, 0.5160329388486451692230830905761645510166025236059793420
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+053, 0.66425798020280820325088307482585132534106704873625388888034286900680
+76152641046  …  1.033333846504426712082580354960107935043970613756493163451
+1294626091384818214, 1.0664686032469082465446852271794933182809166964255378
+32438762276651139095129374, 1.100665855046623660308919551395610359208286716
+684431112070414408183611765253205, 1.13595967174013219044727424686007597453
+6172903481653049159364319427066929995183, 1.1723852156432053491987697297701
+67158307196511889785786439894918782978322870963, 1.209978776582131731617051
+708325497527117244553498434756316642412641437610370797, 1.24877780804833135
+8756513829430099007097842940139504429315922973879445769691784, 1.2888209645
+1229946257972559404143259768018368155787883476891071715795301279543, 1.3301
+48139934054628675268802978666438630864641254421813595879534440847470751688,
+ 1.372800507508458259187806011057611283394590006590596578199873499201906331
+611072], retcode: Success
+Interpolation: 3rd order Hermite
+t: [0.0, 0.0625, 0.125, 0.1875, 0.25, 0.3125, 0.375, 0.4375, 0.5, 0.5625, 0
+.625, 0.6875, 0.75, 0.8125, 0.875, 0.9375, 1.0]
+u: BigFloat[0.50, 0.5325799879535391294151756922663100127575701279367674657
+299889518448727031384926, 0.56728288713718376841017609381133190281668498488
+55565501534311815341659662084392, 0.604247026395540457858840348261076470751
+5845791230606683491210486718827818716904, 0.6436197480773975548106951513331
+34437286938781958375274884622802079377793549762, 0.685557995355440557982096
+349246370736930808950070979750802507189818563351642024, 0.73022893781570593
+36084349405886010308809987247048142151879999305882306169718902, 0.777810637
+810428680311119693945339493753691675945670302006794689942184819812709, 0.82
+849276023042538690428396700476452263279640532871508910845350344109696753782
+66, 0.882477328526228669757698486772395431354193449529466082277853631417758
+5961942936, 0.9399795299915405153402248568618947272920440084137115643604676
+307008419853257788, 1.00122857351893604093217965458142490311824502494352804
+9619445960282439336451516, 1.0664686032469082465446724238467060826602271350
+5450493171046906577618017533485, 1.1359596717401321904472594727959625271540
+69506739201242159983984002811333382739, 1.209978776582131731617034761065124
+311009358614495571372335128166979326800445978, 1.28882096451229946257970625
+3102020998553494397009716401282671347081826473196884, 1.3728005075084582591
+87784036450083092262707343306282981254591926965493411372691]], Dict{Any,Any
+}(:l∞ => BigFloat[3.3543545459629930177501679382781291302012408187338947472
+46416797762893693012556e-49, 5.07977773973643850037988739563364757867015516
+067866884666732578123388975047482e-45, 6.9650533073686584465398166666312934
+86902250519752824131061460869466635839790668e-41, 6.99855995795909600274703
+1148778557831077884643242480170494801380170765753974579e-37, 2.761604674257
+899176583497342905526511107065867988065457455490380825745507598647e-33, 4.9
+650607496729548374201289866032526435726391756486604232601712118906759519607
+09e-28, 2.19751040342660991781470263264956056068365936768378032463580161029
+7349872909655e-23],:final => BigFloat[3.35435454596299301775016793827812913
+0201240818733894747246416797762893693012556e-49, 5.079777739736438500379887
+39563364757867015516067866884666732578123388975047482e-45, 6.96505330736865
+8446539816666631293486902250519752824131061460869466635839790668e-41, 6.998
+559957959096002747031148778557831077884643242480170494801380170765753974579
+e-37, 2.7616046742578991765834973429055265111070658679880654574554903808257
+45507598647e-33, 4.96506074967295483742012898660325264357263917564866042326
+0171211890675951960709e-28, 2.197510403426609917814702632649560560683659367
+683780324635801610297349872909655e-23],:l2 => BigFloat[1.557658061895966325
+846207347700821566122250234951867982385249845278493662676944e-49, 2.3604116
+57197547333498547223212880765989953910523198376084992961121455787643313e-45
+, 3.24060760516074676637178554271828070823716806609832930426777898390162348
+7961701e-41, 3.264565979149024498598621687244084221464920048688554495210368
+172485686228822379e-37, 1.2947776667473864852636114197311110560713898649841
+76915402703871046417929063523e-33, 2.35148503019100306142594944698233564880
+1181524332244933545614443786091245762492e-28, 1.061501597814768635894514677
+590712762248364686527596359902826841740549975688161e-23]), 7, Dict(:dts => 
+[0.0009765625, 0.001953125, 0.00390625, 0.0078125, 0.015625, 0.03125, 0.062
+5]), Dict{Any,Any}(:l∞ => 14.2933275461038524350008931328481604055650481625
+4374715376150534187461411604701,:final => 14.293327546103852435000893132848
+16040556504816254374715376150534187461411604701,:l2 => 14.30280974051840423
+232019057634315242594313233119811212889763182960978082577156), [0.000976562
+5, 0.001953125, 0.00390625, 0.0078125, 0.015625, 0.03125, 0.0625])
 

 
 
@@ -792,10 +1048,7 @@ 
Convergence Test

 

 
 
-
-ERROR: UndefVarError: sim not defined
-

-
+
 
 
This is a clear trend indicating that the convergence is truly Order 14, which is the estimated slope.

 
@@ -828,6 +1081,7 @@ 
Convergence Test

 
Status `/builds/JuliaGPU/DiffEqTutorials.jl/tutorials/ode_extras/Project.toml`
 [f3b72e0c-5b89-59e1-b016-84e28bfd966d] DiffEqDevTools 2.22.0
+[0c46a032-eb83-5123-abaf-570d42b7fbaa] DifferentialEquations 6.14.0
 [961ee093-0014-501f-94e3-6117800e7a78] ModelingToolkit 3.11.0
 [76087f3c-5699-56af-9a33-bf431cd00edd] NLopt 0.6.0
 [2774e3e8-f4cf-5e23-947b-6d7e65073b56] NLsolve 4.4.0
diff --git a/markdown/ode_extras/01-ModelingToolkit.md b/markdown/ode_extras/01-ModelingToolkit.md
index 791d4186..0e6406d5 100644
--- a/markdown/ode_extras/01-ModelingToolkit.md
+++ b/markdown/ode_extras/01-ModelingToolkit.md
@@ -818,6 +818,7 @@ Package Information:
 ```
 Status `/builds/JuliaGPU/DiffEqTutorials.jl/tutorials/ode_extras/Project.toml`
 [f3b72e0c-5b89-59e1-b016-84e28bfd966d] DiffEqDevTools 2.22.0
+[0c46a032-eb83-5123-abaf-570d42b7fbaa] DifferentialEquations 6.14.0
 [961ee093-0014-501f-94e3-6117800e7a78] ModelingToolkit 3.11.0
 [76087f3c-5699-56af-9a33-bf431cd00edd] NLopt 0.6.0
 [2774e3e8-f4cf-5e23-947b-6d7e65073b56] NLsolve 4.4.0
diff --git a/markdown/ode_extras/02-feagin.md b/markdown/ode_extras/02-feagin.md
index 8cbae22e..bcf76b85 100644
--- a/markdown/ode_extras/02-feagin.md
+++ b/markdown/ode_extras/02-feagin.md
@@ -12,52 +12,72 @@ We can use Feagin's order 16 method as follows. Let's use a two-dimensional line
 
 ````julia
 using DifferentialEquations
-````
-
-
-````
-Error: ArgumentError: Package DifferentialEquations not found in current pa
-th:
-- Run `import Pkg; Pkg.add("DifferentialEquations")` to install the Differe
-ntialEquations package.
-````
-
-
-
-````julia
 const linear_bigα = big(1.01)
 f(u,p,t) = (linear_bigα*u)
 
 # Add analytical solution so that errors are checked
 f_analytic(u0,p,t) = u0*exp(linear_bigα*t)
 ff = ODEFunction(f,analytic=f_analytic)
-````
-
-
-````
-Error: UndefVarError: ODEFunction not defined
-````
-
-
-
-````julia
 prob = ODEProblem(ff,big(0.5),(0.0,1.0))
-````
-
-
-````
-Error: UndefVarError: ODEProblem not defined
-````
-
-
-
-````julia
 sol = solve(prob,Feagin14(),dt=1//16,adaptive=false);
 ````
 
 
 ````
-Error: UndefVarError: Feagin14 not defined
+retcode: Success
+Interpolation: 3rd order Hermite
+t: 17-element Array{Float64,1}:
+ 0.0
+ 0.0625
+ 0.125
+ 0.1875
+ 0.25
+ 0.3125
+ 0.375
+ 0.4375
+ 0.5
+ 0.5625
+ 0.625
+ 0.6875
+ 0.75
+ 0.8125
+ 0.875
+ 0.9375
+ 1.0
+u: 17-element Array{BigFloat,1}:
+ 0.50
+ 0.532579987953539129415175692266310012757570127936767465729988951844872703
+1384926
+ 0.567282887137183768410176093811331902816684984885556550153431181534165966
+2084392
+ 0.604247026395540457858840348261076470751584579123060668349121048671882781
+8716904
+ 0.643619748077397554810695151333134437286938781958375274884622802079377793
+549762
+ 0.685557995355440557982096349246370736930808950070979750802507189818563351
+642024
+ 0.730228937815705933608434940588601030880998724704814215187999930588230616
+9718902
+ 0.777810637810428680311119693945339493753691675945670302006794689942184819
+812709
+ 0.828492760230425386904283967004764522632796405328715089108453503441096967
+5378266
+ 0.882477328526228669757698486772395431354193449529466082277853631417758596
+1942936
+ 0.939979529991540515340224856861894727292044008413711564360467630700841985
+3257788
+ 1.001228573518936040932179654581424903118245024943528049619445960282439336
+451516
+ 1.066468603246908246544672423846706082660227135054504931710469065776180175
+33485
+ 1.135959671740132190447259472795962527154069506739201242159983984002811333
+382739
+ 1.209978776582131731617034761065124311009358614495571372335128166979326800
+445978
+ 1.288820964512299462579706253102020998553494397009716401282671347081826473
+196884
+ 1.372800507508458259187784036450083092262707343306282981254591926965493411
+372691
 ````
 
 
@@ -68,7 +88,11 @@ println(sol.errors)
 
 
 ````
-Error: UndefVarError: sol not defined
+Dict{Symbol,BigFloat}(:l∞ => 2.19751040342660991781470263264956056068365936
+7683780324635801610297349872909655e-23,:final => 2.197510403426609917814702
+632649560560683659367683780324635801610297349872909655e-23,:l2 => 1.0615015
+97814768635894514677590712762248364686527596359902826841740549975688161e-23
+)
 ````
 
 
@@ -94,22 +118,17 @@ The error for Feagin's method when the stepsize is 1/16 is 8 orders of magnitude
 
 ````julia
 sol =solve(prob,Feagin14());
-````
-
-
-````
-Error: UndefVarError: Feagin14 not defined
-````
-
-
-
-````julia
 println(sol.errors); print("The length was $(length(sol))")
 ````
 
 
 ````
-Error: UndefVarError: sol not defined
+Dict{Symbol,BigFloat}(:l∞ => 1.54573888394314096254653759860975921981641479
+0728029220638828884206395861982752e-09,:final => 1.545738883943140962546537
+598609759219816414790728029220638828884206395861982752e-09,:l2 => 8.9250668
+70202330409924421192162193462506388332261074725109949218067763405137993e-10
+)
+The length was 3
 ````
 
 
@@ -130,7 +149,243 @@ sim = test_convergence(dts,prob,Feagin14())
 
 
 ````
-Error: UndefVarError: Feagin14 not defined
+DiffEqDevTools.ConvergenceSimulation{DiffEqBase.ODESolution{BigFloat,1,Arra
+y{BigFloat,1},Array{BigFloat,1},Dict{Symbol,BigFloat},Array{Float64,1},Arra
+y{Array{BigFloat,1},1},DiffEqBase.ODEProblem{BigFloat,Tuple{Float64,Float64
+},false,DiffEqBase.NullParameters,DiffEqBase.ODEFunction{false,typeof(Main.
+##WeaveSandBox#258.f),LinearAlgebra.UniformScaling{Bool},typeof(Main.##Weav
+eSandBox#258.f_analytic),Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,No
+thing,Nothing,Nothing,Nothing,Nothing},Base.Iterators.Pairs{Union{},Union{}
+,Tuple{},NamedTuple{(),Tuple{}}},DiffEqBase.StandardODEProblem},OrdinaryDif
+fEq.Feagin14,OrdinaryDiffEq.InterpolationData{DiffEqBase.ODEFunction{false,
+typeof(Main.##WeaveSandBox#258.f),LinearAlgebra.UniformScaling{Bool},typeof
+(Main.##WeaveSandBox#258.f_analytic),Nothing,Nothing,Nothing,Nothing,Nothin
+g,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{BigFloat,1},Array{
+Float64,1},Array{Array{BigFloat,1},1},OrdinaryDiffEq.Feagin14ConstantCache{
+BigFloat,Float64}},DiffEqBase.DEStats}}(DiffEqBase.ODESolution{BigFloat,1,A
+rray{BigFloat,1},Array{BigFloat,1},Dict{Symbol,BigFloat},Array{Float64,1},A
+rray{Array{BigFloat,1},1},DiffEqBase.ODEProblem{BigFloat,Tuple{Float64,Floa
+t64},false,DiffEqBase.NullParameters,DiffEqBase.ODEFunction{false,typeof(Ma
+in.##WeaveSandBox#258.f),LinearAlgebra.UniformScaling{Bool},typeof(Main.##W
+eaveSandBox#258.f_analytic),Nothing,Nothing,Nothing,Nothing,Nothing,Nothing
+,Nothing,Nothing,Nothing,Nothing,Nothing},Base.Iterators.Pairs{Union{},Unio
+n{},Tuple{},NamedTuple{(),Tuple{}}},DiffEqBase.StandardODEProblem},Ordinary
+DiffEq.Feagin14,OrdinaryDiffEq.InterpolationData{DiffEqBase.ODEFunction{fal
+se,typeof(Main.##WeaveSandBox#258.f),LinearAlgebra.UniformScaling{Bool},typ
+eof(Main.##WeaveSandBox#258.f_analytic),Nothing,Nothing,Nothing,Nothing,Not
+hing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{BigFloat,1},Arr
+ay{Float64,1},Array{Array{BigFloat,1},1},OrdinaryDiffEq.Feagin14ConstantCac
+he{BigFloat,Float64}},DiffEqBase.DEStats}[retcode: Success
+Interpolation: 3rd order Hermite
+t: [0.0, 0.0009765625, 0.001953125, 0.0029296875, 0.00390625, 0.0048828125,
+ 0.005859375, 0.0068359375, 0.0078125, 0.0087890625  …  0.9912109375, 0.992
+1875, 0.9931640625, 0.994140625, 0.9951171875, 0.99609375, 0.9970703125, 0.
+998046875, 0.9990234375, 1.0]
+u: BigFloat[0.50, 0.5004934073532741442240167407783486492180603021615841294
+52202794115660211219599, 0.500987301608180818440355281223188950584910597683
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+15, 0.504458235058501913934559188511648417802868424125759953366000451921798
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+951153177861472631409617242, 1.36335493031101930838372463784595682752195537
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+, 1.37280050750845825918780601155411735836188549033294491231479506286094526
+5969766], retcode: Success
+Interpolation: 3rd order Hermite
+t: [0.0, 0.001953125, 0.00390625, 0.005859375, 0.0078125, 0.009765625, 0.01
+171875, 0.013671875, 0.015625, 0.017578125  …  0.982421875, 0.984375, 0.986
+328125, 0.98828125, 0.990234375, 0.9921875, 0.994140625, 0.99609375, 0.9980
+46875, 1.0]
+u: BigFloat[0.50, 0.5009873016081808184403552812231889505849105976869970947
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+2, 0.5089562218366775389970434828264868922469483072826175429449686273069735
+423750136  …  1.34864301545859247967509602307176367401641641210475048875695
+337449929440786918, 1.35130605029464067315359841454792588096269341231012308
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+372800507508458259187806011554117358361885495412387216596637263939057644809
+585], retcode: Success
+Interpolation: 3rd order Hermite
+t: [0.0, 0.00390625, 0.0078125, 0.01171875, 0.015625, 0.01953125, 0.0234375
+, 0.02734375, 0.03125, 0.03515625  …  0.96484375, 0.96875, 0.97265625, 0.97
+65625, 0.98046875, 0.984375, 0.98828125, 0.9921875, 0.99609375, 1.0]
+u: BigFloat[0.50, 0.5019765527452926697413863031219664328338089596679027919
+888741103974398448576829, 0.50396091901209518746154563970525241120918092433
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+837, 0.51807287149253063717412013329248710548519771111335349047947245099497
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+32283726], retcode: Success
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+t: [0.0, 0.015625, 0.03125, 0.046875, 0.0625, 0.078125, 0.09375, 0.109375, 
+0.125, 0.140625  …  0.859375, 0.875, 0.890625, 0.90625, 0.921875, 0.9375, 0
+.953125, 0.96875, 0.984375, 1.0]
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+27, 1.372800507508458259187806011554114596757211232433432893362855858032659
+14211007], retcode: Success
+Interpolation: 3rd order Hermite
+t: [0.0, 0.03125, 0.0625, 0.09375, 0.125, 0.15625, 0.1875, 0.21875, 0.25, 0
+.28125  …  0.71875, 0.75, 0.78125, 0.8125, 0.84375, 0.875, 0.90625, 0.9375,
+ 0.96875, 1.0]
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+Interpolation: 3rd order Hermite
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+.625, 0.6875, 0.75, 0.8125, 0.875, 0.9375, 1.0]
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+}(:l∞ => BigFloat[3.3543545459629930177501679382781291302012408187338947472
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+e-37, 2.7616046742578991765834973429055265111070658679880654574554903808257
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+, 3.24060760516074676637178554271828070823716806609832930426777898390162348
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+590712762248364686527596359902826841740549975688161e-23]), 7, Dict(:dts => 
+[0.0009765625, 0.001953125, 0.00390625, 0.0078125, 0.015625, 0.03125, 0.062
+5]), Dict{Any,Any}(:l∞ => 14.2933275461038524350008931328481604055650481625
+4374715376150534187461411604701,:final => 14.293327546103852435000893132848
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+232019057634315242594313233119811212889763182960978082577156), [0.000976562
+5, 0.001953125, 0.00390625, 0.0078125, 0.015625, 0.03125, 0.0625])
 ````
 
 
@@ -146,11 +401,7 @@ plot(sim)
 ````
 
 
-````
-Error: UndefVarError: sim not defined
-````
-
-
+![](figures/02-feagin_6_1.png)
 
 
 
@@ -191,6 +442,7 @@ Package Information:
 ```
 Status `/builds/JuliaGPU/DiffEqTutorials.jl/tutorials/ode_extras/Project.toml`
 [f3b72e0c-5b89-59e1-b016-84e28bfd966d] DiffEqDevTools 2.22.0
+[0c46a032-eb83-5123-abaf-570d42b7fbaa] DifferentialEquations 6.14.0
 [961ee093-0014-501f-94e3-6117800e7a78] ModelingToolkit 3.11.0
 [76087f3c-5699-56af-9a33-bf431cd00edd] NLopt 0.6.0
 [2774e3e8-f4cf-5e23-947b-6d7e65073b56] NLsolve 4.4.0
diff --git a/markdown/ode_extras/figures/02-feagin_6_1.png b/markdown/ode_extras/figures/02-feagin_6_1.png
new file mode 100644
index 00000000..45202945
Binary files /dev/null and b/markdown/ode_extras/figures/02-feagin_6_1.png differ
diff --git a/pdf/ode_extras/01-ModelingToolkit.pdf b/pdf/ode_extras/01-ModelingToolkit.pdf
index 1f4bf8ae..897c4e7a 100644
Binary files a/pdf/ode_extras/01-ModelingToolkit.pdf and b/pdf/ode_extras/01-ModelingToolkit.pdf differ
diff --git a/pdf/ode_extras/02-feagin.pdf b/pdf/ode_extras/02-feagin.pdf
index cc4d8c19..ff83958d 100644
Binary files a/pdf/ode_extras/02-feagin.pdf and b/pdf/ode_extras/02-feagin.pdf differ
diff --git a/tutorials/ode_extras/Project.toml b/tutorials/ode_extras/Project.toml
index b13e7664..9e93eada 100644
--- a/tutorials/ode_extras/Project.toml
+++ b/tutorials/ode_extras/Project.toml
@@ -1,6 +1,6 @@
 [deps]
-DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
 DiffEqDevTools = "f3b72e0c-5b89-59e1-b016-84e28bfd966d"
+DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
 NLopt = "76087f3c-5699-56af-9a33-bf431cd00edd"