International Journal of Applied Mathematics, Computational Science and Systems Engineering
E-ISSN: 2766-9823
Volume 6, 2024
Computational Techniques for Accurate Solutions of Astrophysical Problems Using Transform-Based Collocation
Authors: , ,
Abstract: This study applies three advanced techniques based on transforms to find approximate solutions to
the Lane-Emden type equation, which is often encountered in mathematical physics and astrophysics. The
proposed methods utilize new trial functions derived from expressing the second-order derivative of the
variable function y(x) using Bernoulli polynomials, and applying Laplace, Sumudu, and differential
transforms. To assess the effectiveness of the proposed methods, the study establishes an error analysis and
stability analysis, and provides numerical examples demonstrating their accuracy and efficiency. In addition, a
comparison of the absolute errors is made among the three methods, namely, Laplace Transform Bernoulli
Collocation Method (LTBCM), Sumudu Transform Bernoulli Collocation Method (STBCM), and Differential
Transform Bernoulli Collocation Method (DTBCM), and with those obtained from prior literature. The results
show that all three methods perform very well in terms of efficiency and accuracy, and can be considered as
suitable techniques for solving the Lane-Emden type equation.
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Keywords: Fins problem, homotopy perturbation method, Laplace and differential transform methods,
boundary value problems, polynomial projection
Pages: 119-136
DOI: 10.37394/232026.2024.6.11