whether meshes affect computational step lengths in pdepe

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feynman feynman 2024-1-19

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编辑： Torsten 2024-1-20

In pdepe the user specifies an xmesh and tmesh. Do these meshes affect what meshes and computational step lengths adopted by the solver and hence the error? In other words are the computational step lengths self adaptive as in ode23 etc?

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Torsten 2024-1-19

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编辑：Torsten 2024-1-19

Adaptive in x: no. Adaptive in t: yes. Thus the x-mesh affects computational accuracy, the t-mesh not. The accuracy in t is influenced as usual by the relative and absolute tolerances in the "odeset".

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feynman feynman 2024-1-20

Maybe you are talking about accuracy rather than convergence? As I understand it spatial discretization affects accuracy but not convergence. To have two spatial discretization points over 100 m won't yield divergence if a fine mesh is convergent.

Torsten 2024-1-20

编辑：Torsten 2024-1-20

A complicated profile of a function can only be reconstructed by its spatial derivatives if there are enough supporting points. Thus convergence to the solution of a complicated function can only be achieved if the x-mesh is chosen fine enough.

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