Please explain how to solve coupled equation in MATLAB? ODE 45 or Runge kutta method? The equation is d/dz(Ep) + (n/c) d/dt (Ep) = Es M where n= 1.45 and C = 3e8

%Non Linear ODE equation

clc;

clear all;

%code is incomplete, i was trying to explore but couldnt figure it out properly

c=3e8;

A= 86;

n= 1.45;

g= 1.92e-11;

i= 1;

M= i.* g .* A ;

V= n/ c;

syms z t;

f = @(z,t) ;

Answer 1

[Torsten]

The equation you posted is a PDE, not an ODE. So an ODE integrator cannot be used directly for its solution.

You will have to discretize the equation in the z-coordinate and solve the resulting system of ordinary differential equations using ODE15S. Look up "method-of-lines" and "upwind scheme" for more information.

If all variables except E_p and your boundary condition at z=0 are constant, the equation can be solved analytically.