[Fishy]

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[FMDenaro]

Originally Posted by Fishy

Hi all,

I am using the thomas algorithm to solve a linear implicit scheme with a dirichlet boundary condition at x=0 and a neumann boundary condition at x=1. However, the maximum error obtained decreases at first before increasing in magnitude with increasing discretization in space (time discretization was kept constant). Why is this so?

The implicit scheme was obtained using an euler backward scheme in time and a centred approximation to the second derivative in space).

I assume you have no bug in the code (Thomas solver and BCs., space and time discretization) but this is always something to carefully consider.
Then, the convergence analysis requires theoretically that grid size and time step go to zero in such a way that dt/h= constant. You have to reduce the dt when you refine the grid size.
If you take dt=constant, you can see a level of the discretization error that does not decrease anymore owing to the constant part of the local truncation error.
Could you also give details about the analytical solution you are using?