The applicability of the method is shown by two test problems and acquired results show that the method is good accuracy and efficiency.
📌 3 Maddede Bu Makale
🎯
Amaç & Hipotez: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.
📊
Temel Bulgular & Veri:Firstly, we present the ultraspherical wavelets, then the corresponding operational matrix of integration is presented.
💡
Sonuç & Katkı:The applicability of the method is shown by two test problems and acquired results show that the method is good accuracy and efficiency.
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.
OZDEMIR, N., SECER, A. (2021). 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 Sayı: 3, 1307–1319. https://ajindex.com/articles/897433
Dehghan M. and Shokri A., (2009) Numerical solution of the nonlinear Klein–Gordon equation using radial basis functions, Journal of Computational and Applied Mathematics, 230(2), 400-410
Wazwaz A. M., (2006) The modified decomposition method for analytic treatment of differential equations, Applied Mathematics and Computation, 173(1), 165-176
Bülbül B., & Sezer M., (2013) A new approach to numerical solution of nonlinear Klein-Gordon equation, Mathematical Problems in Engineering, 2013
Sadigh B. S., (2011), Numerical Solution Of Klein-Gordon Equation By Using The Adomian’s Decomposition And Variational Iterative Methods, Int. J. Industrial Mathematics,79-89
Hepson O. E., Korkmaz A., & Dag I., (2018) On the numerical solution of the Klein-Gordon equation by exponential cubic B-spline collocation method, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 412-421
Bildik N., & Deniz S., (2020) New approximate solutions to the nonlinear Klein-Gordon equations using perturbation iteration techniques, Discrete & Continuous Dynamical Systems-S, 13(3), 503
Yusufoğlu E., (2008) The variational iteration method for studying the Klein–Gordon equation, Applied Mathematics Letters, 21(7), 669-674
Han H., & Zhang Z., (2009) An analysis of the finite-difference method for one-dimensional Klein–Gordon equation on unbounded domain, Applied numerical mathematics, 59(7), 1568-1583
Kaya D., & El-Sayed S. M., (2004) A numerical solution of the Klein–Gordon equation and convergence of the decomposition method, Applied mathematics and computation, 156(2), 341-353
Ebaid A., (2009) Exact solutions for the generalized Klein–Gordon equation via a transformation and Exp-function method and comparison with Adomian’s method, Journal of Computational and Applied Mathematics, 223(1), 278-290
Wang T. M., & Zhu J. M., (2009) New explicit solutions of the Klein–Gordon equation using the variational iteration method combined with the Exp-function method, Computers & Mathematics with Applications, 58(11-12), 2444-2448
Secer A., & Ozdemir N., (2019) An effective computational approach based on Gegenbauer wavelets for solving the time-fractional Kdv-Burgers-Kuramoto equation, Advances in Difference Equations, 2019(1), 386
Ozdemir N., Secer A., & Bayram M., (2019) The Gegenbauer Wavelets-Based Computational Methods for the Coupled System of Burgers’ Equations with Time-Fractional