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Optimal superconvergent one step quadratic spline collocation methods. (English) Zbl 1155.65089

Summary: We formulate new optimal quadratic spline collocation methods for the solution of various elliptic boundary value problems in the unit square. These methods are constructed so that the collocation equations can be solved using a matrix decomposition algorithm. The results of numerical experiments exhibit the expected optimal global accuracy as well as superconvergence phenomena.

MSC:

65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations

Software:

FFTPACK; FISHPAK
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Full Text: DOI

References:

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