Automatic Reformulation of ODEs to Systems of First-Order Equations
Article No.: 31, Pages 1 - 18
Abstract
Most numerical ODE solvers require problems to be written as systems of first-order differential equations. This normally requires the user to rewrite higher-order differential equations as coupled first-order systems. Here, we introduce the treeVar class, written in object-oriented Matlab, which is capable of algorithmically reformulating higher-order ODEs to equivalent systems of first-order equations. This allows users to specify problems using a more natural syntax and saves them from having to manually derive the first-order reformulation. The technique works by using operator overloading to build up syntax trees of expressions as mathematical programs are evaluated. It then applies a set of rules to the resulting trees to obtain the first-order reformulation, which is returned as another program. This technique has connections with algorithmic/automatic differentiation. We present how treeVar has been incorporated in Chebfun, greatly improving the ODE capabilities of the system.
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Index Terms
- Automatic Reformulation of ODEs to Systems of First-Order Equations
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September 2018
291 pages
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Association for Computing Machinery
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Publication History
Published: 03 January 2018
Accepted: 01 November 2017
Revised: 01 January 2017
Received: 01 January 2016
Published in TOMS Volume 44, Issue 3
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- The MathWorks, Inc
- European Research Council under the European Union's Seventh Framework Programme
- ERC
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