- #1

oddiseas

- 73

- 0

## Homework Statement

__[t]=-U+k__

__[xx] u(x,0)=U(L,0)=0 u(x,0)sin(pix/L)__

Write down difference equations for the approximate solution of this problem using the following methods:

1)forward difference

2)backward difference

3)crank nicholson

I can do part 3, but i am stuck on the first two methods. I can find an exppression for the partial derivative of t, but the second derivative using the forward difference from a taylor approximation is 0 isn't it?

F(x+dx,t)=f(x,t)+[f][x](x,t)dx+[f][xx](x,t)(dx)^2

which if u solve for f''=0

Write down difference equations for the approximate solution of this problem using the following methods:

1)forward difference

2)backward difference

3)crank nicholson

## Homework Equations

I can do part 3, but i am stuck on the first two methods. I can find an exppression for the partial derivative of t, but the second derivative using the forward difference from a taylor approximation is 0 isn't it?

F(x+dx,t)=f(x,t)+[f][x](x,t)dx+[f][xx](x,t)(dx)^2

which if u solve for f''=0