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

Jonas Berx; Joseph O. Indekeu

doi:10.1016/j.padiff.2022.100392

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arXiv · 2205.08823

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

Jonas Berx·Joseph O. Indekeu

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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.

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Jonas Berx, Joseph O. Indekeu. 2022-05-18. The BLUES function method for second-order partial differential equations: application to a nonlinear telegrapher equation. https://doi.org/10.1016/j.padiff.2022.100392

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