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‎doc/pub/tutorial/README‎

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This directory contains the odespy for the package.
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The documentation is automatically generated by ../src/odespy/make.sh.
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This directory contains published versions of the tutorial for the odespy
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package.
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* html: sphinx version
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* odespy.pdf: classic LaTeX version
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* odespy.html: HTML bootstrap
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* odespy-solarized.html: HTML w/solarized colors
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The files are automatically generated by ../src/odespy/make.sh.

‎doc/pub/tutorial/html/.buildinfo‎

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# Sphinx build info version 1
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# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
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config: a74edf7a1082bd945a5d91292d4f73f8
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config: 12abf71e4135ce40f5edc02b03cdfd5a
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tags: 645f666f9bcd5a90fca523b33c5a78b7

‎doc/pub/tutorial/html/_sources/main_odespy.txt‎

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.. Automatically generated Sphinx-extended reStructuredText file from DocOnce source
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(https://github.com/hplgit/doconce/)
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.. !split
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.. Document title:
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A Tutorial for the Odespy Interface to ODE Solvers
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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:Authors: Hans Petter Langtangen, Liwei Wang
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:Date: Mar 15, 2015
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:Date: Apr 14, 2015
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The Odespy package makes it easy to specify an ODE problem in
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Python and get it solved by a wide variety of different numerical
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methods and software.
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.. _ode:sec:motivation:
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.. !split
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Motivation
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==========
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FORTRAN codes one can also implement the problem in FORTRAN and avoid
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callback to Python.
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Installation
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============
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Basic Usage
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===========
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a user-defined function ``terminate`` that can be used to implement
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a criterion for terminating the solution process.
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Mathematically, the relevant criterion is
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:math:`||u-R||<\hbox{tol}`, where tol is an acceptable
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:math:`||u-R|| < \hbox{tol}`, where tol is an acceptable
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tolerance, say :math:`100` in the present case where :math:`R=10^5`.
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The ``terminate`` function implements the criterion
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and returns true if the criterion is met:
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def terminate(u, t, step_no):
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"""u[step_no] holds (the most recent) solution at t[step_no]."""
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return abs(u[step_no] - R) < tol:
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return abs(u[step_no] - R) < tol
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Note that the simulation is anyway stopped for :math:`t > T` so :math:`T`
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must be large enough for the termination criterion to be reached (if not,
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def terminate(u, t, step_no):
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"""u[step_no] holds (the most recent) solution at t[step_no]."""
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return abs(u[step_no] - R) < tol:
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return abs(u[step_no] - R) < tol
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u, t = solver.solve(time_points, terminate)
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print 'Final u(t=%g)=%g' % (t[-1], u[-1])
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The module ``odespy.problems`` contains many predefined ODE problems.
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Using Adaptive Methods
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----------------------
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Adaptive Methods
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----------------
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The solvers used in the previous examples have all employed a constant
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time step :math:`\Delta t`. Many solvers available through the Odespy
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The complete code is available in `sode.py <https://github.com/hplgit/odespy/blob/master/doc/src/tutorial/src-odespy/sode1.py>`__.
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Inner Workings of the Package
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=============================
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J = np.eye(self.neq) - dt*self.jac(ukp1, t[n+1])
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return F, J
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Troubleshooting
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===============
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‎doc/pub/tutorial/html/_static/cbc_banner.png‎

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‎doc/pub/tutorial/html/_static/default.css‎

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