The BLUES function method for second-order partial differential equations: Application to a nonlinear telegrapher equation

An analytic iteration sequence based on the extension of BLUES (Beyond Linear Use Equation Superposition) function method to partial differential equations (PDEs) with second-order time derivatives is studied. The original formulation modified by introducing a matrix formalism that takes into account initial conditions for higher-order derivatives. both solution and its now play role source vector. tested nonlinear telegrapher equation, which can be reduced wave equation suitable choice parameters. In addition, comparison made three other methods: Adomian decomposition method, variational (with Green function) homotopy perturbation method. shown worthwhile alternative methods.