Premium
A Spline Difference Scheme on a Piecewise Equidistant Grid
Author(s) -
Surla K.,
Uzelac Z.
Publication year - 1997
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19970771206
Subject(s) - equidistant , discretization , mathematics , piecewise , spline (mechanical) , rate of convergence , mathematical analysis , uniform convergence , norm (philosophy) , singular perturbation , quadratic equation , grid , perturbation (astronomy) , geometry , computer science , computer network , channel (broadcasting) , physics , structural engineering , bandwidth (computing) , quantum mechanics , law , political science , engineering
We consider singularly perturbed boundary value problems of reaction‐diffusion type and their discretization via quadratic spline difference schemes on a piecewise equidistant mesh of the Shishkin type. On such a mesh we prove that a solution to the discretisation is almost second order accurate in the discrete maximum norm, uniformly in the perturbation parameter. Numerical results are presented, which verify this rate of convergence.