A NUMERICAL ALGORITHM BASED ON ULTRASPHERICAL WAVELETS FOR SOLUTION OF LINEAR AND NONLINEAR KLEIN-GORDON EQUATIONS

ÖZDEMİR N., SEÇER A.

SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI, vol.38, no.3, pp.1307-1319, 2020 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 3
  • Publication Date: 2020
  • Journal Name: SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Academic Search Premier, Directory of Open Access Journals
  • Page Numbers: pp.1307-1319
  • Keywords: Ultraspherical wavelets, Klein-Gordon equation, Galerkin method, operational matrix of integration, VOLTERRA INTEGRAL-EQUATIONS
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper, Galerkin method based on the Ultraspherical wavelets expansion together with operational matrix of integration is developed to solve linear and nonlinear Klein Gordon (KG) equations with the given initial and boundary conditions. Firstly, we present the ultraspherical wavelets, then the corresponding operational matrix of integration is presented. To transform the given PDE into a system of linear-nonlinear algebraic equations which can be efficiently solved by suitable solvers, we utilize the operational matrix of integration and both properties of Ultraspherical wavelets. The applicability of the method is shown by two test problems and acquired results show that the method is good accuracy and efficiency.