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A combination of spline and spectral approximation for a class of singularly perturbed problems
Author(s) -
Adžić Ne V.,
Uzelac Zor.
Publication year - 1998
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.19980781502
Subject(s) - spline (mechanical) , mathematics , spectral method , collocation (remote sensing) , chebyshev filter , thin plate spline , mathematical analysis , chebyshev polynomials , function (biology) , spline interpolation , computer science , statistics , structural engineering , machine learning , evolutionary biology , engineering , bilinear interpolation , biology
We shall consider the selfadjoint boundary layer problem described by the second order differential equation with a small parameter multiplying the highest derivative. The approximate solution will be constructed by the use of spline collocation technique out of the layer and by the use of truncated Chebyshev series inside the layer. The layer subinterval is determined by the use of resemblence function in terms of the chosen degree of the spectral solution. The error at the division point is estimated by the use of the error of the spline function, and it is used to obtain the error estimate inside the layer. Numerical example shows that the combination of these two techniques gives better results than the application of modified spectral methods.