I am trying to write a program using Maple software,
the sys of delay DEs are simplified in the form
x'=constant * x(t-tau)+nonlinear function1 of x(t) and, y(t)
y'=constant* y(t-tau)+ nonlinear function2 of x(t)and y(t)
t is the time from 0 to t_N, x'=dx/dt, tau is the delay, ICs are x(0)=y(0)=0
Mathematica did it and worked fine after the assumption
x(-tau->0)=y(-tau->0)=t^2 worked. Maple's company said they
have no subroutine to do it.
Any help will be highly appreciated
Dear Hanan,
if you are willing to solve the problem namely by MAPLE and MAPLE has no built subroutines for it, I suppose the simplest way is to use the so-called "step method". Divide the interval of t's on which you want to solve your DE into subintervals [-tau,0], [0, tau], [tau, 2tau], [2tau, 3tau] etc. Then resolve DE first on the interval [0,tau] taking into account that x(t-tau) and y(t-tau) in this case are KNOWN - they are defined by the initial conditions. Then, to find solutions on the interval [tau, 2tau] you again solve non-delaed DE, sinse in this case again x(t-tau) and y(t-tau) are already known, etc.
This procedure looks may be programmed as a cycle very easily.
Hope, this helps you. Good luck!
Sorry: This procedure looks cumbersome, but may be programmed as a cycle very easily.
I will try that..the DDEs have a special way to be dealt with, I am still new in this field. Thank you
Simply my dear because I don't have it. I have Maple Pro. In fact Mathematica solve it nicely no problem. The Maple-Soft company had told me that there is no command to do it, but I thought there might be someone who've done it.
In MATLAB, the function "dde23" solve the initial value problems for delay differential equations with constant delays.
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