Coupled Equations with spatial and time evolution using ode45
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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
回答（1 个）
Torsten
2017-1-18
0 个投票
Split in real and imaginary part and solve the system of 4 equations using pdepe.
Best wishes
Torsten.
6 个评论
Pavan Kumar
2017-1-18
Torsten
2017-1-18
Yes, by using the method of lines. But pdepe will save you from using this error-prone procedure.
Best wishes
Torsten.
Pavan Kumar
2017-1-19
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
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
2017-1-25
Torsten
2017-1-25
Never heard of this method - sorry.
Best wishes
Torsten.
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2017-1-18
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