Coupled Equations with spatial and time evolution using ode45

Hii Friends,

I have the following set of coupled equations.

where 'T' is time and 'Z' is distance.

Can anyone give me a hint on how to solve these equations using ODE45.

Thanking you.

Pavan

Answer 1

[Torsten]

Split in real and imaginary part and solve the system of 4 equations using pdepe.

Best wishes

Torsten.

[Pavan Kumar]

Thanks Torsten for the suggestion. Can this type of equations be solved via ode45?

[Torsten]

Yes, by using the method of lines. But pdepe will save you from using this error-prone procedure.

Best wishes

Torsten.

[Pavan Kumar]

Hii Torsten

great help from you.Thanks a lot.Little more changes.

Using ode45 i was able to solve the below equations which excludes 'T' derivates.

du1dz(1) = 1i*a*B2*conj(B1)*exp(1i*1*delk*z); du2dz(2) = 1i*a*B1*B1*exp(-1i*1*delk*z);

Now i need to include 'T' derivatives as below.

Can you suggest me.

Pavan

[Torsten]

Look up "methods of lines" for the solution of partial differential equations.

You will have to discretize the T-interval of integration:

Tstart=T0<T1<T2<...<TN=Tend

Then in each grid point Ti, approximate the partial derivatives as

d^2u/dT^2 approximately (u(i+1)-2*u(i)+u(i-1))/deltaT^2
du/dT approximately (u(i+1)-u(i-1))/(2*deltaT)

The whole process will result in a system of ordinary differential equations for u in the grid points.

Best wishes

Torsten.

[Pavan Kumar]

Hii Torsten, Can these equations be solved using split step fourier method. My professor has adviced me using that since it is much easier and faster.

Any help would be really fruitful

[Torsten]

Never heard of this method - sorry.

Best wishes

Torsten.