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
dsys ≔ ⅆ2ⅆ t2 yt + yt−110=0, y0=1, y'0=0
dsys:=ⅆ2ⅆt2yt+yt−110=0,y0=1,Dy0=0
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 = −xt−12−exp−t2, x0=1
dsys_var:=ⅆⅆtxt=−xt−12−12ⅇ−t,x0=1
max_delay ≔ fsolvet = 12+exp−t2, t;
max_delay:=0.7388350311
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.
dsolve/numeric, dsolve/rkf45, dsolve/ck45, dsolve/rosenbrock, dsolve/numeric/delay
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