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

Abstract

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

8 pages, 3 figures

References in corpus (3)

• The BLUES function method applied to partial differential equations and analytic approximants for interface growth under shear
• BLUES iteration applied to nonlinear ordinary differential equations for wave propagation and heat transfer
• Epidemic processes with vaccination and immunity loss studied with the BLUES function method