Numerical solution of singular regular boundary value problems by pole detection with qd-algorithm

In this paper, we present a method using qd-algorithm combined with finite difference method for numerically solving singular boundary value problems for certain ordinary differential equation having singular coefficients. (We can also use qd-algorithm combined with other numerical methods.) These p...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 233; no. 2; pp. 420 - 436
Main Authors: Allouche, H., Marhraoui, N.
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 15.11.2009
Elsevier
Subjects:
Boundary value problems
Degenerate problems
Exact sciences and technology
Finite difference scheme
Formally orthogonal Hadamard polynomials
Fröbenius method
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Pole detection
qd-Algorithm
Sciences and techniques of general use
Singularity
65L06
Singularity
Boundary value problems
65L07
Degenerate problems
Fröbenius method
Finite difference scheme
Formally orthogonal Hadamard polynomials
65L Except 65L05
65L70
65L80
65L20
65L12
Pole detection
qd-Algorithm
Difference scheme
Differential equation
Singular equation
Singular value
Numerical method
Partial differential equation
Numerical solution
Initial value problem
Regular solution
Algorithm
Orthogonal polynomial
Degenerate equation
Numerical analysis
Boundary value problem
Applied mathematics
Problem solving
Finite difference method
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Description
Summary:In this paper, we present a method using qd-algorithm combined with finite difference method for numerically solving singular boundary value problems for certain ordinary differential equation having singular coefficients. (We can also use qd-algorithm combined with other numerical methods.) These problems arise when reducing partial differential equation to ordinary differential equation by physical symmetry. Some illustrative examples are given to demonstrate the efficiency and high accuracy of the proposed method and compare it to the numerical results made with other methods.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2009.07.036