Approximate solution of the damped Burgers equation

Malfliet, W.

doi:10.1088/0305-4470/26/16/003

Cited by 38 publications

(18 citation statements)

References 6 publications

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“…This is so indeed because one can note that the most approaches to search exact solutions of nonlinear ordinary differential equations are based on general solution of the Riccati equation. The application of the tanh method confirms this idea [24,28,29,31,32]. This is due to the fact that the Riccati equation is simplest equation of first order of polynomial form that have the Painleve property [10,17,21].…”

Section: Methods Appliedmentioning

confidence: 74%

Nonlinear Differential Equations With Exact Solutions Expressed Via The Weierstrass Function

Kudryashov

2004

Zeitschrift Für Naturforschung A

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New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption that nonlinear differential equations have exact solution which is general solution of the simplest integrable equation. The Riccati equation is shown to be a building block to find a lot of nonlinear differential equations with exact solutions. Nonlinear differential equations of the second, third and fourth order with special solutions are given. Most of these equations are used at the description of processes in physics and in theory of nonlinear waves.

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Section: Methods Appliedmentioning

confidence: 74%

Nonlinear Differential Equations With Exact Solutions Expressed Via The Weierstrass Function

Kudryashov

2004

Zeitschrift Für Naturforschung A

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“…In this article the bisection method [14] has been used to solve Eq. (18). In the present case, the initial condition was chosen as f 0 (x) ϭ sech 2 x.…”

Section: Marker Methods For Burgers' Equationmentioning

confidence: 99%

A marker method for the solution of the damped Burgers' equation

Lewandowski

2005

Numerical Methods Partial

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A new method for the solution of the damped Burgers' equation is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details. The marker method is applicable to a general class of nonlinear dispersive partial differential equations.

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“…Now we describe the hyperbolic function method (Bai, 2001;Khater et al, 2001aKhater et al, , 2004bMalfliet, 1991Malfliet, , 1992Malfliet, , 1993Malfliet, , 2004Malfliet and Hereman, 1996a,b), for a given NLPDE, say, in two variables, f (u, u x , u t , u xx , u xt , u tt …”

Section: Traveling Wave Solutions For Some Nlpdesmentioning

confidence: 99%

Conservation Laws and Exact Solutions for some Nonlinear Partial Differential Equations

2006

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is used for finding the local conservation laws for some nonlinear partial differential equations. The method does not require the use or existence of a variational principle and reduces the calculation of conservation laws to solving a system of linear determining equations similar to that of finding symmetries. An explicit construction formula is derived which yields a conservation law for each solution of the determining system. Different methods to construct new exact solution classes for the same nonlinear partial differential equations are also presented, which are named hyperbolic function method and the Bäcklund transformations. On the other hand, other methods and transformations are developed to obtain exact solutions for some nonlinear partial differential equations.

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Approximate solution of the damped Burgers equation

Cited by 38 publications

References 6 publications

Nonlinear Differential Equations With Exact Solutions Expressed Via The Weierstrass Function

Nonlinear Differential Equations With Exact Solutions Expressed Via The Weierstrass Function

A marker method for the solution of the damped Burgers' equation

Conservation Laws and Exact Solutions for some Nonlinear Partial Differential Equations

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