Solution of Klein-Gordon Equation by a Method of Lines Using Reproducing Kernel Hilbert Space Method (Journal of Partial Differential Equations, 2024)
This paper presents a method of lines solution based on the reproducingkernel Hilbert space method to the nonlinear one-dimensional Klein-Gordon equationthat arises in many scientific fields areas. Our method uses discretization of the partialderivatives of the space variable to get a system of ODEs in the time variable and thensolve the system of ODEs using reproducing kernel Hilbert space method. Considertwo examples to validate the proposed method. Compare the results with the exactsolution by calculating the error norms $L_2$ and $L_∞$ at various time levels. The resultsshow that the presented scheme is a systematic, effective and powerful technique forthe solution of Klein-Gordon equation.