Time-space pseudospectral algorithm for numerical solution of Sine/Klein-Gordon equations

Abstract

In this research article, we present spectrally accurate time-space pseudospectral method to approximate the solution of one-dimensional Sine/Klein-Gordon equations. The proposed method is implemented on Chebyshev-Gauss-Lobatto points to study the solitary soliton wave solutions. In the numerical scheme, an algebraic mapping is used to convert non-homogeneous problem into homogeneous problem and the nonlinear Sine/Klein-Gordon equations are reduced to system of nonlinear algebraic equations, which are further solved by Newton Raphson method. Interaction of kink and solitary soliton solutions are tested to demonstrate the performance of the proposed method. The efficiency and accuracy for the proposed method have been calculated via L2 and L∞-norms and found competent results as compared to analytical solution and other existing numerical methods. The proposed method succeeds to obtain high order rate of convergence.