Lie symmetry analysis, soliton and numerical solutions of boundary value problem for variable coefficients coupled KdV–Burgers equation

Vikas Kumar, Aisha Alqahtani

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

Abstract

In this article, an initial and boundary value problem for variable coefficients coupled KdV–Burgers equation is considered. With the help of Lie group approach, initial and boundary value problem for variable coefficients coupled KdV–Burgers equation reduced to an initial value problem for nonlinear third-order ordinary differential equations (ODEs). Moreover, the systems of ODEs are solved to obtain soliton solutions. Further, classical fourth-order Runge–Kutta method is applied to systems of ODEs for constructing numerical solutions of coupled KdV–Burgers equation. Numerical solutions are computed, and accuracy of numerical scheme is assessed by applying the scheme half mesh principal to calculate maximum errors.

Original languageEnglish
Pages (from-to)2903-2915
Number of pages13
JournalNonlinear Dynamics
Volume90
Issue number4
DOIs
Publication statusPublished - 1 Dec 2017

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Lie Symmetry
Initial value problems
Soliton Solution
Solitons
Variable Coefficients
Ordinary differential equations
Boundary value problems
Initial Value Problem
Boundary Value Problem
Numerical Solution
System of Ordinary Differential Equations
Lie groups
Third Order Differential Equation
Runge-Kutta Methods
Numerical Scheme
Fourth Order
Ordinary differential equation
Mesh
Calculate

Keywords

  • Coupled KdV–Burgers equation
  • Lie symmetry analysis
  • Numerical solution
  • Soliton solution

Cite this

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abstract = "In this article, an initial and boundary value problem for variable coefficients coupled KdV–Burgers equation is considered. With the help of Lie group approach, initial and boundary value problem for variable coefficients coupled KdV–Burgers equation reduced to an initial value problem for nonlinear third-order ordinary differential equations (ODEs). Moreover, the systems of ODEs are solved to obtain soliton solutions. Further, classical fourth-order Runge–Kutta method is applied to systems of ODEs for constructing numerical solutions of coupled KdV–Burgers equation. Numerical solutions are computed, and accuracy of numerical scheme is assessed by applying the scheme half mesh principal to calculate maximum errors.",
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Lie symmetry analysis, soliton and numerical solutions of boundary value problem for variable coefficients coupled KdV–Burgers equation. / Kumar, Vikas; Alqahtani, Aisha.

In: Nonlinear Dynamics, Vol. 90, No. 4, 01.12.2017, p. 2903-2915.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Alqahtani, Aisha

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N2 - In this article, an initial and boundary value problem for variable coefficients coupled KdV–Burgers equation is considered. With the help of Lie group approach, initial and boundary value problem for variable coefficients coupled KdV–Burgers equation reduced to an initial value problem for nonlinear third-order ordinary differential equations (ODEs). Moreover, the systems of ODEs are solved to obtain soliton solutions. Further, classical fourth-order Runge–Kutta method is applied to systems of ODEs for constructing numerical solutions of coupled KdV–Burgers equation. Numerical solutions are computed, and accuracy of numerical scheme is assessed by applying the scheme half mesh principal to calculate maximum errors.

AB - In this article, an initial and boundary value problem for variable coefficients coupled KdV–Burgers equation is considered. With the help of Lie group approach, initial and boundary value problem for variable coefficients coupled KdV–Burgers equation reduced to an initial value problem for nonlinear third-order ordinary differential equations (ODEs). Moreover, the systems of ODEs are solved to obtain soliton solutions. Further, classical fourth-order Runge–Kutta method is applied to systems of ODEs for constructing numerical solutions of coupled KdV–Burgers equation. Numerical solutions are computed, and accuracy of numerical scheme is assessed by applying the scheme half mesh principal to calculate maximum errors.

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