A NUMERICAL ALGORITHM BASED ON ULTRASPHERICAL WAVELETS FOR SOLUTION OF LINEAR AND NONLINEAR KLEIN-GORDON EQUATIONS
SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES, cilt.38, sa.3, ss.1307-1319, 2020 (ESCI)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 38 Sayı: 3
- Basım Tarihi: 2020
- Dergi Adı: SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Academic Search Premier, Directory of Open Access Journals
- Sayfa Sayıları: ss.1307-1319
- İstanbul Gelişim Üniversitesi Adresli: Hayır
Özet
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.