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A Comparative Survey of Numerical Methods for the Linear Generalized Abel Integral Equation
Author(s) -
Te Riele H. J. J.,
Schroevers Ph.
Publication year - 1986
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.19860660306
Subject(s) - collocation (remote sensing) , smoothness , collocation method , mathematics , orthogonal collocation , order (exchange) , product (mathematics) , mathematical analysis , computer science , differential equation , geometry , ordinary differential equation , machine learning , economics , finance
A numerical comparison is made between a number of important representatives of the following classes of methods: (i) collocation, (ii) product integration and (iii) global methods. Special attention is paid to the performance of these methods for problems with a non‐smooth solution. It turned out that, when only relatively low accuracy is required, a good choice would be a second or third order collocation method of Branca. — A new collocation method which accounts for possible non‐smoothness of the solution near the origin, turned out to be advantageous when high accuracy is required, both for problems with a non‐smooth solution, and for problems with a smooth solution.