Abstract
Purpose - In this article, the authors have proposed a numerical scheme based on forward finite difference, quasilinearization process and polynomial differential quadrature method (PDQM) to find the numerical solutions of nonlinear Klein-Gordon equation with Dirichlet and Neumann boundary condition.Design/methodology/approach - In first step, time derivative is discretized by forward difference method. Then, quasilinearization process is used to tackle the non-linearity in the equation. Finally, fully discretization by differential quadrature method leads to a system of linear equations which is solved by Gauss-elimination method. Findings - The accuracy of the proposed method is demonstrated by several test examples. The numerical results are found to be in good agreement with the exact solutions and the numerical solutions exist in literature. The proposed scheme can be expended for multidimensional problems.Originality/value - The main advantage of the present scheme is that the scheme gives very accurate and similar results to the exact solutions by choosing less number of grid points. Secondly, the scheme gives better accuracy than [25, 30] by choosing less number of grid points and big time step length . Also, the scheme can be extended for multidimensional problems.
Purpose - In this article, the authors have proposed a numerical scheme based on forward finite difference, quasilinearization process and polynomial differential quadrature method (PDQM) to find the numerical solutions of nonlinear Klein-Gordon equation with Dirichlet and Neumann boundary condition.Design/methodology/approach - In first step, time derivative is discretized by forward difference method. Then, quasilinearization process is used to tackle the non-linearity in the equation. Finally, fully discretization by differential quadrature method leads to a system of linear equations which is solved by Gauss-elimination method. Findings - The accuracy of the proposed method is demonstrated by several test examples. The numerical results are found to be in good agreement with the exact solutions and the numerical solutions exist in literature. The proposed scheme can be expended for multidimensional problems.Originality/value - The main advantage of the present scheme is that the scheme gives very accurate and similar results to the exact solutions by choosing less number of grid points. Secondly, the scheme gives better accuracy than [25, 30] by choosing less number of grid points and big time step length . Also, the scheme can be extended for multidimensional problems.
