An Accurate Numerical Algorithm for Solving Singular and Nonsingular System of Initial Value Problems on Large Interval

In this article, a numerical algorithm for solving both linear and nonlinear system of initial problems is proposed. Chebyshev wavelet finite difference (CWFD) method is indeed a hybrid of Chebyshev wavelets and finite difference methods. The exploitation of the useful properties of Chebyshev wavele...

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Bibliographic Details
Published inMediterranean journal of mathematics Vol. 13; no. 6; pp. 5033 - 5051
Main Authors Kazemi Nasab, A., Pashazadeh Atabakan, Z., Ismail, A. I.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2016
Springer Nature B.V
Subjects
Boundary value problems
Chebyshev approximation
Finite difference method
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear programming
Nonlinear systems
Numerical analysis
Wavelet analysis
singular ODEs
65L05
Chebyshev wavelet finite difference method
65L80
Chebyshev wavelets
65D15
65L12
system of ordinary differential equations
Chebyshev polynomials
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Summary:In this article, a numerical algorithm for solving both linear and nonlinear system of initial problems is proposed. Chebyshev wavelet finite difference (CWFD) method is indeed a hybrid of Chebyshev wavelets and finite difference methods. The exploitation of the useful properties of Chebyshev wavelets and finite difference method results in the reduction of the computation of the problem to a set of algebraic equations which can be more easily solved. Several examples of singular and nonsingular systems are included to illustrate the efficiency and accuracy of the proposed method.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-016-0790-9