An efficient approach for solving Klein–Gordon equation arising in quantum field theory using wavelets

A new approach for the solution of Klein–Gordon equation using Legendre wavelet-based approximation method is presented. The properties of Legendre wavelets are used to reduce the problem to the solution of system of algebraic equations. Usually 2 ( k - 1 ) M 2 connection coefficients are required to solve the Klein–Gordon equation by Legendre wavelets method as mentioned in the literature. But, our proposed method based on Legendre wavelets and algebraic polynomials require only 2 ( k - 1 ) M connection coefficients instead of 2 ( k - 1 ) M 2 . Also the convergence analysis and error estimation for the proposed function approximation through the truncated series have been discussed and approved with the exact solution. Illustrative examples are discussed to demonstrate the validity and applicability of the technique with lesser computational effort.