second order differential equation are arranged in ring

mi (d^tδi/dt^2) + di(dδi/dt) = pmi − b sin(δi) − bint [sin(δi − δi+1) + sin(δi − δi−1)] where mi=1,di=0.3,b=1,bint=100,pmi=0.95 and i=1 to 1000. intial conditions are 1. how do i solve it. second order derivative term is mi(d^tδi/dt^2) and first order is di(dδi/dt).

Answer 1

[John D'Errico]

Your problem is this is not a classic differential equation. It is a delay-difference equation, also known as a difference-differential equation.

The standard ODE solver tools like ODE45 are not able to handle it. Instead, you need to use tools designed to solve that problem, such as dde23.

https://www.mathworks.com/help/matlab/delay-differential-equations.html

There will be examples in the docs. Read them.

[Torsten]

My guess is that it is a system of ODEs for delta(1),delta(2),...,delta(1000).

ODE45 seems applicable to solve it.

Best wishes

Torsten.

[satyavir yadav]

yes sir ode15s can solve it but how can i write function for this problem.