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Question regarding xmesh option in pdepe solver

Asked by Deepa Maheshvare on 1 Jan 2019
Latest activity Commented on by Deepa Maheshvare on 2 Jan 2019
The command xmesh is given as an input to the pdepe solver.
For example
xmesh = 1:1:10
Does this mean the solver internally sets the spacial discretization = xmesh (if no, how is the spacial direction dicretized?)/
Is it just the points at which solution is output?


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I'm slightly confused with the descriptions given here.Is "tmesh" the points at which the solution is output?
I suppose the discretization in time domain is performed using variable step sizes based on the tolerance that is defined by the user. If I understand correctly, the discretization space is set by the user and not computed by the solver.
"pdepe" uses the method of lines to solve PDEs. Thus the spatial derivatives are approximated on the "xmesh" defined by the user. The resulting set of ordinary differential equations in time is solved by ODE15S, a general ODE integrator. Thus the "tmesh" you prescribe is only used for outputting purposes. Time integration is done adaptively - the temporal mesh can only be influenced indirectly by the user via the choice of RelTol and AbsTol.

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