An effective approach for numerical solution of linear and nonlinear singular boundary value problems


Saldır O., Sakar M. G.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.46, no.1, pp.1395-1410, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.1002/mma.8769
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.1395-1410
  • Keywords: reproducing kernel method, singular nonlinear boundary value problems, shifted Legendre polynomials, FINITE-DIFFERENCE METHOD, B-SPLINE COLLOCATION, REPRODUCING KERNEL, CUBIC SPLINE, LEGENDRE, EQUATION
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this study, an effective approach is presented to obtain a numerical solution of linear and nonlinear singular boundary value problems. The proposed method is constructed by combining reproducing kernel and Legendre polynomials. Legendre basis functions are used to get the kernel function, and then the approximate solution is obtained as a finite series sum. Comparison of numerical results is made with the results obtained by other methods available in the literature. Furthermore, efficiency and accuracy of the method are demonstrated in tabulated results and plotted graphs. The numerical outcomes demonstrate that our method is very effective, applicable, and convenient.