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Some remarks about the collocation method on a modified Legendre grid. (English) Zbl 0868.65049
Summary: We compare the results obtained by applying the standard collocation method at the Legendre Gauss-Lobatto nodes, for a model problem simulating a steady advection-diffusion equation, with those obtained by collocating at a new set of nodes. These nodes are derived from a suitable modification of the Legendre grid, according to the magnitude of the ratio between the advective and the diffusive parts of the differential operator.

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
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