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ODE-toolbox: Automatic selection and generation of integration schemes for systems of ordinary differential equations

Linssen, Charl; Morrison, Abigail; Eppler, Jochen Martin


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        <foaf:name>Eppler, Jochen Martin</foaf:name>
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    <dct:title>ODE-toolbox: Automatic selection and generation of integration schemes for systems of ordinary differential equations</dct:title>
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    <dcat:keyword>differential equation</dcat:keyword>
    <dcat:keyword>ODE</dcat:keyword>
    <dcat:keyword>numerical integration</dcat:keyword>
    <dcat:keyword>simulation</dcat:keyword>
    <dcat:keyword>solver</dcat:keyword>
    <dcat:keyword>propagator matrix</dcat:keyword>
    <dcat:keyword>symbolic analysis</dcat:keyword>
    <dcat:keyword>dynamic system</dcat:keyword>
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    <dct:description>&lt;p&gt;Choosing the optimal solver for systems of ordinary differential equations (ODEs) is a critical step in dynamical systems simulation. ODE-toolbox is a Python package that assists in solver benchmarking, and recommends solvers on the basis of a set of user-configurable heuristics. For all dynamical equations that admit an analytic solution, ODE-toolbox generates propagator matrices that allow the solution to be calculated at machine precision. For all others, first-order update expressions are returned based on the Jacobian matrix.&lt;/p&gt; &lt;p&gt;In addition to continuous dynamics, discrete events can be used to model instantaneous changes in system state, such as a neuronal action potential. These can be generated by the system under test, as well as applied as external stimuli, making ODE-toolbox particularly well-suited for applications in computational neuroscience.&lt;/p&gt;</dct:description>
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