Approximate solution of singular IVPs of Lane–Emden type and error estimation via advanced Adomian decomposition method

This article aims to present a simple and effective method, named as advanced Adomian decomposition method, to attain the approximate solution of singular initial value problems of Lane–Emden type. Also, convergence analysis and error analysis with an upper bound of the absolute error for the propos...

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Bibliographic Details
Published in:Journal of applied mathematics & computing Vol. 66; no. 1-2; pp. 527 - 542
Main Authors: Umesh, Kumar, Manoj
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2021
Springer Nature B.V
Subjects:
Applied mathematics
Approximation
Boundary value problems
Computational Mathematics and Numerical Analysis
Decomposition
Error analysis
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical methods
Original Research
Theory of Computation
Upper bounds
Lane–Emden equation
Adomian polynomials
Advanced Adomian decomposition method
Convergence theorem
Error bound
Singular initial-value problems
Residual error
65N20
ISSN:1598-5865, 1865-2085
Online Access:Get full text
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Summary:This article aims to present a simple and effective method, named as advanced Adomian decomposition method, to attain the approximate solution of singular initial value problems of Lane–Emden type. Also, convergence analysis and error analysis with an upper bound of the absolute error for the proposed method are discussed. The proposed method is capable to remove the singular behaviour of the problems and provides an approximate solution up to the desired order. To illustrate the reliability and validity of the proposed method with error estimate several examples that arise in applications are considered and the attained outcomes are compared with some existing numerical methods.
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ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-020-01444-2