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On the convergence of a high-accuracy compact conservative scheme for the modified regularized long-wave equation.

Pan X, Zhang L - Springerplus (2016)

Bottom Line: In this article, we develop a high-order efficient numerical scheme to solve the initial-boundary problem of the MRLW equation.The scheme consists of a fourth-order compact finite difference approximation in space and a version of the leap-frog scheme in time.The unique solvability of numerical solutions is shown.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematics and Information Science, Weifang University, Weifang, 261061 China ; School of Management, Qufu Normal University, Rizhao, 276800 China.

ABSTRACT
In this article, we develop a high-order efficient numerical scheme to solve the initial-boundary problem of the MRLW equation. The method is based on a combination between the requirement to have a discrete counterpart of the conservation of the physical "energy" of the system and finite difference method. The scheme consists of a fourth-order compact finite difference approximation in space and a version of the leap-frog scheme in time. The unique solvability of numerical solutions is shown. A priori estimate and fourth-order convergence of the finite difference approximate solution are discussed by using discrete energy method and some techniques of matrix theory. Numerical results are given to show the validity and the accuracy of the proposed method.

No MeSH data available.


Exact solutions u(x, t) at  and numerical solutions  computed by the scheme (11)–(14) with  at  and 10
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Fig3: Exact solutions u(x, t) at and numerical solutions computed by the scheme (11)–(14) with at and 10

Mentions: The curves of the solitary wave with time computed by scheme (11) with and are given in Fig. 3; the waves at and 10 agree with the ones at quite well, which also demonstrate the accuracy and efficiency of the scheme in present paper.


On the convergence of a high-accuracy compact conservative scheme for the modified regularized long-wave equation.

Pan X, Zhang L - Springerplus (2016)

Exact solutions u(x, t) at  and numerical solutions  computed by the scheme (11)–(14) with  at  and 10
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4835426&req=5

Fig3: Exact solutions u(x, t) at and numerical solutions computed by the scheme (11)–(14) with at and 10
Mentions: The curves of the solitary wave with time computed by scheme (11) with and are given in Fig. 3; the waves at and 10 agree with the ones at quite well, which also demonstrate the accuracy and efficiency of the scheme in present paper.

Bottom Line: In this article, we develop a high-order efficient numerical scheme to solve the initial-boundary problem of the MRLW equation.The scheme consists of a fourth-order compact finite difference approximation in space and a version of the leap-frog scheme in time.The unique solvability of numerical solutions is shown.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematics and Information Science, Weifang University, Weifang, 261061 China ; School of Management, Qufu Normal University, Rizhao, 276800 China.

ABSTRACT
In this article, we develop a high-order efficient numerical scheme to solve the initial-boundary problem of the MRLW equation. The method is based on a combination between the requirement to have a discrete counterpart of the conservation of the physical "energy" of the system and finite difference method. The scheme consists of a fourth-order compact finite difference approximation in space and a version of the leap-frog scheme in time. The unique solvability of numerical solutions is shown. A priori estimate and fourth-order convergence of the finite difference approximate solution are discussed by using discrete energy method and some techniques of matrix theory. Numerical results are given to show the validity and the accuracy of the proposed method.

No MeSH data available.