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Singularly Perturbed Spline Difference Schemes on a Non‐Equidistant Grid
Author(s) -
Surla K.,
Stojanović M.
Publication year - 1988
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.19880680317
Subject(s) - equidistant , mathematics , grid , spline (mechanical) , mathematical analysis , constant (computer programming) , geometry , boundary value problem , combinatorics , physics , computer science , thermodynamics , programming language
An exponentially fitted spline difference scheme on a non‐equidistant grid is formed for solving the singularly perturbed two point boundary value problem: ϵy″ + p(x) y′ = f(x), 0 < x < 1,0 < ϵ ≪1, y(0) = α 0 , y(1) = α 1 , p(x) ≧ p > 0. Uniform convergence of first order is proved under the condition on the grid: 0 ≦ h i − h i−1 ≦ M i h i−1 max(x i , ϵ), h i =x i+1 − x i , 0 = x 0 < x 1 <… < x n+1 = 1, 0 ≦ M i ≦ M, M is a constant independent of h i and ϵ. Numerical examples are given, too.