Variable precision arithmetic in ode45 and others?

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Michael Croucher
Michael Croucher 2020-10-29
评论： Walter Roberson 2022-6-23
Is it possible to use vpa in ordinary differential equation solvers like ode45?

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Walter Roberson
Walter Roberson 2020-10-29
编辑：Walter Roberson 2020-10-30
Sort of. The internal symbolic engine has two numeric ode routines. At the moment I do not know if there is a matlab level interface to those routines.
You might need to use feval(symengine) to access the routines.
http://www.cfm.brown.edu/people/dobrush/am33/MuPad/MuPad22.html
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Walter Roberson
Walter Roberson 2022-6-23
Mathworks said that those routines are gone and will not be back.

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John D'Errico
John D'Errico 2020-10-29
Short answer - no.
Long answer - nnnnoooooo.
ODE45 uses only singles or doubles. Nothing symbolic. vpa is a symbolic tool.
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John D'Errico
John D'Errico 2020-10-29
I suppose it may happen one day. For example, vpaintegral appeared a few years ago. They could provide a tool to do the same for an ODE. But I don't see it happening soon.

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Steven Lord
Steven Lord 2020-10-30
What types of differential equations are you trying to solve that you need to use arbitrary precision arithmetic?
If you're trying to solve the ODE symbolically rather than numerically, take a look at the dsolve function in Symbolic Math Toolbox.
If you have computed a symbolic equation for the right-hand side of your system of ODEs, you can convert that into a form that the numeric ODE solvers in MATLAB (like ode45) can accept that operates on double arrays using odeFunction also in Symbolic Math Toolbox.
This documentation page may be of interest.

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