TY - JOUR
T1 - The BLUES function method for second-order partial differential equations
T2 - Application to a nonlinear telegrapher equation
AU - Berx, Jonas
AU - Indekeu, Joseph O.
N1 - Publisher Copyright:
© 2022 The Author(s)
PY - 2022/6
Y1 - 2022/6
N2 - 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.
AB - 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.
KW - Analytic iteration
KW - BLUES function method
KW - Telegrapher equation
U2 - 10.1016/j.padiff.2022.100392
DO - 10.1016/j.padiff.2022.100392
M3 - Journal article
AN - SCOPUS:85131375547
SN - 2666-8181
VL - 5
JO - Partial Differential Equations in Applied Mathematics
JF - Partial Differential Equations in Applied Mathematics
M1 - 100392
ER -