how to solve four sets of ode having four variables

The distinction in my question is that I need to put up such code with convective terms. As a student of MATLAB I have not been able to find such answers from past questions in the manner below. All derivatives are with respect to time. The variables are p, q, r, s. The equations are:

d^2p/dt^2 + d^2r/dt^2 +d^2s/dt^2 = p + 2*q + 3*r + 4*s

d^2q/dt^2 + d^2r/dt^2 +d^2s/dt^2 = p + 2*q + 3*r + 4*s

d^2p/dt^2 + d^2q/dt^2 + d^2r/dt^2 +d^2s/dt^2 = p + 2*q + 3*r + 4*s - 5*dr/dt - 5*ds/dt

d^2p/dt^2 + d^2q/dt^2 + d^2r/dt^2 +d^2s/dt^2 = p + 2*q + 3*r + 4*s - 5*dr/dt - 5*ds/dt

Initial conditions are all zero at t =dt = 0, i.e. p(0)=q(0)=r(0)=s(0) = 0. and dp(0)/dt=dq(0)/dt=dr(0)/dt=ds(0)/dt=0

I have spent a great deal of time trying with ode45. I need help on this, thanks in advance!

Answer 1

[Steven Lord]

Use the "Example: Nonstiff van der Pol Equation" example on this documentation page to rewrite each of your higher order ODEs into a system of first order ODEs (potentially with a mass matrix.) Then solve that larger system.

However, if we look at your equations, I suspect you're going to get nowhere fast. All your initial conditions (both the "position" and "velocity" terms being 0 at t = 0) makes me suspect you may only have the solution where all your functions are {p, q, r, s}(t) = 0.

The fact that your third and fourth equations are the same is also slightly suspicious.

[Vincent Ike]

Thank you Mr. Steven. I'll do some more study following your suspicions. Thanks for the clues also.

[Vincent Ike]

You are right. I think only r(0)=diff(r(0))=0. But you can play with the initial conditions.

[Vincent Ike]

The link you shared helped. Many thanks sir.

[Steven Lord]

You're welcome.