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## Main Question or Discussion Point

I'm a bit stuck with using the C-N method

The question I'm trying to solve is the standard heat equation with:

U=[sin(pi)*x] at [itex]\tau[/itex] = 0

& U = 0 at x = 0

& x = 1 for [itex]\tau \geq 0[/itex]

The intervals are 0.2 in x AND 0.02 in [itex]\tau[/itex] up to [itex]\tau[/itex] = 0.06

I've been asked to solve using an Explicit which I've done using formula derived from the taylor theorem, but the second part is asking to use the C-N Method.

I started using this formula:
in matrix form, where I'm letting r = 0.5 using

The only thing that's concerning me is that it seems a bit long winded and the answers for U(i,j) that have arisen don't seem at all close to the explicit method.

I put it all in matrix form and then using Gaussian elimination, is the correct method?

The question I'm trying to solve is the standard heat equation with:

U=[sin(pi)*x] at [itex]\tau[/itex] = 0

& U = 0 at x = 0

& x = 1 for [itex]\tau \geq 0[/itex]

The intervals are 0.2 in x AND 0.02 in [itex]\tau[/itex] up to [itex]\tau[/itex] = 0.06

I've been asked to solve using an Explicit which I've done using formula derived from the taylor theorem, but the second part is asking to use the C-N Method.

I started using this formula:

The only thing that's concerning me is that it seems a bit long winded and the answers for U(i,j) that have arisen don't seem at all close to the explicit method.

I put it all in matrix form and then using Gaussian elimination, is the correct method?