An Integral Equation Formalism for Integrating a Nonlinear Initial-Boundary Value Problem for a Boussinesq Equation

In this paper, a new nonlinear initial-boundary value problem for a Boussinesq equation is formulated. And a coupled system of nonlinear integral equations, equivalent to the new initial-boundary value problem, is constructed for integrating the initial-boundary value problem, but which is inherentl...

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Bibliographic Details
Published inMathematical problems in engineering Vol. 2020; no. 2020; pp. 1 - 20
Main Author Jang, T. S.
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 2020
Hindawi
John Wiley & Sons, Inc
Subjects
Boundary value problems
Boussinesq equations
Computer simulation
Engineering
Exact solutions
Formulas (mathematics)
Formulations
Integral equations
Iterative methods
Nonlinear equations
Solitary waves
Wave propagation
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Summary:In this paper, a new nonlinear initial-boundary value problem for a Boussinesq equation is formulated. And a coupled system of nonlinear integral equations, equivalent to the new initial-boundary value problem, is constructed for integrating the initial-boundary value problem, but which is inherently different from other conventional formulations for integral equations. For the numerical solutions, successive approximations are applied, which leads to a functional iterative formula. A propagating solitary wave is simulated via iterating the formula, which is in good agreement with the known exact solution.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1024-123X
1563-5147
DOI:10.1155/2020/6083128