International Conference on Computational Methods in Applied Sciences, İstanbul, Türkiye, 12 - 16 Temmuz 2019, ss.201
In this study, we apply an effective algorithm to solve the Linear and Nonlinear Klein- Gordon equations, which is based on the Gegenbauer wavelet Galerkin Method. The Klein-Gordon equation is the name given to the equation of motion of a quantum scalar or pseudo scalar field, a field whose quanta are spin-less particles. It describes the quantum amplitude for finding a point particle in various places, the relativistic wave function, but the particle propagates both forwards and backwards in time. The properties of Gegenbauer wavelets were used to transform the Linear and Nonlinear Klein- Gordon equations to a system of nonlinear algebraic equations in the unknown expansion coefficients. The Galerkin method was used to find these coefficients. Some numerical examples are used to illustrate the preciseness and effectiveness of the proposed method. The results show that the Gegenbauer wavelet Galerkin Method is very efficient, simple and can be applied to other nonlinear problems.