Abstract
Two semidiscrete collocation approximations using smooth cubic splines are developed as approximations to the solution of two-point linear parabolic boundary value problems.L ∞-convergence results are presented for these two approximations as well as the piecewise linear Galerkin approximation. Several computational examples are given to illustrate the convergence results and demonstrate the applicability of the method.
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Cavendish, J.C., Hall, C.A. L ∞-convergence of collocation and galerkin approximations to linear two-point parabolic problems. Aeq. Math. 11, 230–249 (1974). https://doi.org/10.1007/BF01834921
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DOI: https://doi.org/10.1007/BF01834921