The BLUES function method for second-order partial differential equations

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

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

The BLUES function method for second-order partial differential equations : Application to a nonlinear telegrapher equation. / Berx, Jonas; Indekeu, Joseph O.

In: Partial Differential Equations in Applied Mathematics, Vol. 5, 100392, 06.2022.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Berx, J & Indekeu, JO 2022, 'The BLUES function method for second-order partial differential equations: Application to a nonlinear telegrapher equation', Partial Differential Equations in Applied Mathematics, vol. 5, 100392. https://doi.org/10.1016/j.padiff.2022.100392

APA

Berx, J., & Indekeu, J. O. (2022). The BLUES function method for second-order partial differential equations: Application to a nonlinear telegrapher equation. Partial Differential Equations in Applied Mathematics, 5, [100392]. https://doi.org/10.1016/j.padiff.2022.100392

Vancouver

Berx J, Indekeu JO. The BLUES function method for second-order partial differential equations: Application to a nonlinear telegrapher equation. Partial Differential Equations in Applied Mathematics. 2022 Jun;5. 100392. https://doi.org/10.1016/j.padiff.2022.100392

Author

Berx, Jonas ; Indekeu, Joseph O. / The BLUES function method for second-order partial differential equations : Application to a nonlinear telegrapher equation. In: Partial Differential Equations in Applied Mathematics. 2022 ; Vol. 5.

Bibtex

@article{d9a2b61fa3c3459b828343e3b6fa9d9b,

title = "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.",

keywords = "Analytic iteration, BLUES function method, Telegrapher equation",

author = "Jonas Berx and Indekeu, {Joseph O.}",

note = "Publisher Copyright: {\textcopyright} 2022 The Author(s)",

year = "2022",

month = jun,

doi = "10.1016/j.padiff.2022.100392",

language = "English",

volume = "5",

journal = "Partial Differential Equations in Applied Mathematics",

issn = "2666-8181",

publisher = "Elsevier",

}

RIS

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.

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

UR - http://www.scopus.com/inward/record.url?scp=85131375547&partnerID=8YFLogxK

U2 - 10.1016/j.padiff.2022.100392

DO - 10.1016/j.padiff.2022.100392

M3 - Journal article

AN - SCOPUS:85131375547

VL - 5

JO - Partial Differential Equations in Applied Mathematics

JF - Partial Differential Equations in Applied Mathematics

SN - 2666-8181

M1 - 100392

ER -

ID: 371847500

Niels Bohr Institute