- #1

- 7

- 0

## Main Question or Discussion Point

Hi, I'm not sure how to solve problems of this form:

Uxx - Ut = h(x,t)

where Uxx is second derivative of U(x,t) wrt x and Ut is first derivative of U(x,t) wrt t.

Boundary conditions are as follows:

U(0,t)=U(a,t)=U(x,0)=0

and h(x,t) is a fairly simple function, or even constant, say h=1.

I'm fine with the homogeneous case except my coefficients don't seem to work when the solution is plotted. No idea how to solve when h(x,t) is anything other than 0 though. I have B&DPi text book here but it isnt very clear. I'm going to keep trying but in the meantime if anyone gets a chance to help me, please do. Particularly for the coefficients as I need to assess the convergence of the solution.

I checked out the tutorial at the top of this forum but it didnt seem to quite have what I'm after. Ah, how I miss the days of solving a simple 1st order ODE.

Thanks in advance.

Uxx - Ut = h(x,t)

where Uxx is second derivative of U(x,t) wrt x and Ut is first derivative of U(x,t) wrt t.

Boundary conditions are as follows:

U(0,t)=U(a,t)=U(x,0)=0

and h(x,t) is a fairly simple function, or even constant, say h=1.

I'm fine with the homogeneous case except my coefficients don't seem to work when the solution is plotted. No idea how to solve when h(x,t) is anything other than 0 though. I have B&DPi text book here but it isnt very clear. I'm going to keep trying but in the meantime if anyone gets a chance to help me, please do. Particularly for the coefficients as I need to assess the convergence of the solution.

I checked out the tutorial at the top of this forum but it didnt seem to quite have what I'm after. Ah, how I miss the days of solving a simple 1st order ODE.

Thanks in advance.