A Numerical Solution for Hirota-Satsuma Coupled KdV Equation

A Petrov-Galerkin method and product approximation technique are used to solve numerically the Hirota-Satsuma coupled Korteweg-de Vries equation, using cubic B -splines as test functions and a linear B -spline as trial functions. The implicit midpoint rule is used to advance the solution in time. Ne...

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Bibliographic Details
Published inAbstract and Applied Analysis Vol. 2014; no. 2014; pp. 962 - 970-1400
Main Authors Ismail, M. S., Ashi, H. A.
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2014
Hindawi Publishing Corporation
Hindawi Limited
Wiley
Subjects
Accuracy
Differential equations, Nonlinear
Differential equations, Partial
Economic models
Finite element analysis
Mathematical research
Numerical analysis
Spline theory
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Summary:A Petrov-Galerkin method and product approximation technique are used to solve numerically the Hirota-Satsuma coupled Korteweg-de Vries equation, using cubic B -splines as test functions and a linear B -spline as trial functions. The implicit midpoint rule is used to advance the solution in time. Newton’s method is used to solve the block nonlinear pentadiagonal system we have obtained. The resulting schemes are of second order accuracy in both directions, space and time. The von Neumann stability analysis of the schemes shows that the two schemes are unconditionally stable. The single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitons, three solitons, and birth of solitons is also discussed.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/819367