Numerical Solutions of ODE with Delay - Maple Programming Help

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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

See Also

Example: Harmonic oscillator with delay

dsys  ⅆ2ⅆ t2 yt + yt110=0, y0=1,  y'0=0

dsys:=ⅆ2ⅆt2yt+yt110=0,y0=1,Dy0=0

(1.1)

dsn  dsolvedsys, numeric:

plots:odeplotdsn,0..10,size=600,golden;

For variable delay, the maximum delay time, which is not always trivial to compute, needs to be provided in the call to dsolve:

dsys_var  ⅆⅆ t xt = xt12expt2, x0=1

dsys_var:=ⅆⅆtxt=xt1212ⅇt,x0=1

(1.2)

max_delay  fsolvet = 12+expt2, t;

max_delay:=0.7388350311

(1.3)

dsn_var  dsolvedsys_var, numeric, delaymax=0.74:

plots:-odeplotdsn_var, 0..5,size=600,golden

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.

See Also

dsolve/numeric, dsolve/rkf45, dsolve/ck45, dsolve/rosenbrock, dsolve/numeric/delay