Galerkin Methods Based on Hermite Splines for Singular Perturbation Problems

DOI10.1137/040607411zbMath1107.65064OpenAlexW1980826771MaRDI QIDQ5470939

Song-Tao Liu, Yuesheng Xu

Publication date: 2 June 2006

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/040607411

zbMATH Keywords

numerical experimentssingular perturbationsboundary layeroptimal order of uniform convergenceelliptic two point boundary value problemsgrid meshes

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Singular perturbations for ordinary differential equations (34E15) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

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Modified hierarchy basis for solving singular boundary value problems ⋮ An efficient superconvergent spline collocation algorithm for solving fourth order singularly perturbed problems ⋮ An exponential spline difference scheme for solving a class of boundary value problems of second-order ordinary differential equations ⋮ $C^1$ spline wavelets on triangulations ⋮ DE-sinc method for second order singularly perturbed boundary value problems ⋮ An improved extrapolated collocation technique for singularly perturbed problems using cubic B-spline functions ⋮ High order finite volume methods for singular perturbation problems ⋮ Graded Galerkin methods for the high-order convection-diffusion problem ⋮ A recent development of computer methods for solving singularly perturbed boundary value problems

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