Numerical solutions of the Burgers–Huxley equation by the IDQ method

Tomasiello, Stefania

doi:10.1080/00207160801968762

Cited by 54 publications

(30 citation statements)

References 14 publications

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“…This equation with p(u) = 2u 2 −u −u 3 = −u(u −1)(u −1) is a special case of FitzHughNagumo equation [6]. The initial condition is taken appropriate with the exact solution [16] u(x, t) = …”

Section: Problemmentioning

confidence: 99%

The differential quadrature solution of nonlinear reaction-diffusion and wave equations using several time-integration schemes

Meral

Tezer‐Sezgin

2011

Int. J. Numer. Meth. Biomed. Engng.

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SUMMARYThree different time-integration schemes, namely the finite difference method (FDM) with a relaxation parameter, the least-squares method (LSM) and the finite element method (FEM), are applied to the differential quadrature (DQM) solution of one-dimensional nonlinear reaction-diffusion and wave equations. In the solution procedure, the space derivatives are discretized using DQM, which may also be used without the need of boundary conditions. The aim of the paper is to find computationally more efficient time-integration algorithm by comparison. For the nonlinear reaction-diffusion equation, which is a parabolic type, FEM is found to be the method of choice in terms of accuracy and computational cost. For the nonlinear wave equation, it is seen that both the FDM and LSM are better than FEM. Therefore, LSM can be preferred as a direct method for the nonlinear wave equation.

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Section: Problemmentioning

confidence: 99%

The differential quadrature solution of nonlinear reaction-diffusion and wave equations using several time-integration schemes

Meral

Tezer‐Sezgin

2011

Int. J. Numer. Meth. Biomed. Engng.

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“…Shu and Richards [20] obtained explicit formulations to compute weighting coefficients using Lagrange interpolation polynomials. In addition, Tomasiello has obtained numerical solutions of Burgers-Huxley Equation by discretizing the equation using DQM both in time and space [21]. Korkmaz and Dag have solved nonlinear Schrödinger equation numerically using both polynomial and cosine expansion-based DQMs [22,23].…”

Section: Introductionmentioning

confidence: 99%

Numerical algorithms for solutions of Korteweg–de Vries equation

Korkmaz¹

2009

Numerical Methods Partial

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The nonlinear Korteweg-de Vries (KdVE) equation is solved numerically using both Lagrange polynomials based differential quadrature and cosine expansion-based differential quadrature methods. The first test example is travelling single solitary wave solution of KdVE and the second test example is interaction of two solitary waves, whereas the other three examples are wave production from solitary waves. Maximum error norm and root mean square error norm are computed, and numerical comparison with some earlier works is done for the first two examples, the lowest four conserved quantities are computed for all test examples.

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“…Tomasiello [15], has got the numerical solutions the Burger-Huxley equation using DQM in both time and space discretizations.…”

Section: Introductionmentioning

confidence: 99%

Cosine expansion‐based differential quadrature algorithm for numerical solution of the RLW equation

Dağ

Korkmaz²,

Saka

2009

Numerical Methods Partial

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The differential quadrature method based on cosine expansion is applied to obtain numerical solutions of the RLW equation. The propagation of single solitary wave is studied to validate the efficiency of the algorithm. Then, test problems including interaction of two and three solitary waves, undulation, and evolution of solitary waves are implemented. Solutions are compared with earlier results. Discrete conservation quantities are computed for test experiments.

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Numerical solutions of the Burgers–Huxley equation by the IDQ method

Cited by 54 publications

References 14 publications

The differential quadrature solution of nonlinear reaction-diffusion and wave equations using several time-integration schemes

The differential quadrature solution of nonlinear reaction-diffusion and wave equations using several time-integration schemes

Numerical algorithms for solutions of Korteweg–de Vries equation

Cosine expansion‐based differential quadrature algorithm for numerical solution of the RLW equation

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