 Numerical Solutions of ODE with Delay - Maple Programming Help

 Numerical Solutions of ODE with Delay

Numeric solutions for initial value problems with ODE/DAE via dsolve[numeric] has been enhanced to accommodate delay terms for the three main variable step integrators, rkf45, ck45, and rosenbrock.

Example: Harmonic oscillator with delay

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 ${\mathrm{dsys}}{:=}\left\{\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{t}}^{{2}}}{}{y}{}\left({t}\right){+}{y}{}\left({t}{-}\frac{{1}}{{10}}\right){=}{0}{,}{y}{}\left({0}\right){=}{1}{,}{\mathrm{D}}{}\left({y}\right){}\left({0}\right){=}{0}\right\}$ (1.1)
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 > $\mathrm{plots}:-\mathrm{odeplot}\left(\mathrm{dsn},0..10,\mathrm{size}=\left[600,"golden"\right]\right);$ For variable delay, the maximum delay time, which is not always trivial to compute, needs to be provided in the call to dsolve:

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 ${\mathrm{dsys_var}}{:=}\left\{\frac{{ⅆ}}{{ⅆ}{t}}{}{x}{}\left({t}\right){=}{-}{x}{}\left({t}{-}\frac{{1}}{{2}}{-}\frac{{1}}{{2}}{}{{ⅇ}}^{{-}{t}}\right){,}{x}{}\left({0}\right){=}{1}\right\}$ (1.2)
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 ${\mathrm{max_delay}}{:=}{0.7388350311}$ (1.3)
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 > Detailed information on this feature, such as setting of initial values, controlling the storage used to retain the delay data, and use with events can be found on the dsolve[numeric][delay] help page.