An effective approach based on Smooth Composite Chebyshev Finite Difference Method and its applications to Bratu-type and higher order Lane-Emden problems


Aydinlik S., Kırış A. , Roul P.

MATHEMATICS AND COMPUTERS IN SIMULATION, vol.202, pp.193-205, 2022 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 202
  • Publication Date: 2022
  • Doi Number: 10.1016/j.matcom.2022.05.032
  • Title of Journal : MATHEMATICS AND COMPUTERS IN SIMULATION
  • Page Numbers: pp.193-205
  • Keywords: Smooth Composite Chebyshev Finite Difference Method, Lane-Emden type of equations, Bratu type of equations, Singular differential equations, Convergence analysis, NUMERICAL-SOLUTION, EQUATIONS, ALGORITHM, MODEL

Abstract

The Smooth Composite Chebyshev Finite Difference method is generalized for higher order initial and boundary value problems. Round-off and truncation error analyses and convergence analysis of the method are also extended to higher order. The proposed method is applied to obtain the highly precise numerical solutions of boundary or initial value problems of the Bratu and higher order Lane Emden types. To visualize the competency of the presented method, the obtained results are compared with nine different methods, namely, Bezier curve method, Adomian decomposition method, Operational matrix collocation method, Direct collocation method, Haar Wavelet Collocation, Bernstein Collocation Method, Improved decomposition method, Quartic B-Spline method and New Cubic B-spline method. The comparisons show that the presented method is highly accurate than the other numerical methods and also gets rid of the singularity of the given problems.(c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.