I have a system of 5 differential equations with 5 unknown variables So I have 4 equations differentiated with respect to time and the 5th equation is a partial differential equation with respect to time and distance. All the equations have variables interdependent with each other. Example:
dF/dt = 3*F + 4*G + Constant; dG/dt = 3*H + 4*G + Constant + F; dH/dt = 3*H + 4*G + Constant + I; dI/dt = 3*H + 4*I + J*5 + Constant; ∂J/∂t = 3*F + 4*H + J + ∂J/∂x;
I am solving this in matlab. I have initial values and boundary conditions and it is differentiated for a period of 24 hours .I tried solving using explicit method,encountered a lot of iteration errors I have also tried solving using implicit finite difference method.But this is not giving me any good results. I have also tried using differential syntax to solve them. I heard about time series,and how does it apply here if possible?Are there any other methods I can approach this system?