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Implicit Finite Difference Scheme for Singularly Perturbed Burger-Huxley Equations

Journal of Partial Differential Equations 2022年第1期35卷 87-100页

作者： KABETO masho jima DURESSA Gemechis File Department of Mathematics College of Natural SciencesJimma UniversityJimmaEthiopia

In this paper,an implicit finite difference scheme is presented to solve one dimensional unsteady singularly perturbed Burger-Huxley *** quadratically convergent quasilinearization technique is used to linearize the nonlinear term of the *** innovative significance of this paper is the procedure to consider initial guesses in order to start the quasilinearization *** basic initial guessing causes to produce a more accurate solutions with the small iteration number for the problem under *** derivatives are replaced by finite difference approximation,then we obtain the two-level time direction and the three-term recurrence relation in the spatial *** convergence analysis of the proposed method has been *** experiments were conducted to support the theoretical ***,the result shows that the proposed method gives a more accurate solution with a higher rate of convergence than some existing methods.

关键词： Singularly perturbed Burger-Huxley equation higher-order accurate solution

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Numerical Solution of the Coupled Viscous Burgers’ Equation Using Differential Quadrature Method Based on Fourier Expansion Basis

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Applied Mathematics 2018年第7期9卷 821-835页

作者： masho jima Alemayehu Shiferaw Ali Tsegaye Department of Mathematics Jimma University Jimma Ethiopia

The differential quadrature method based on Fourier expansion basis is applied in this work to solve coupled viscous Burgers’ equation with appropriate initial and boundary conditions. In the first step for the given problem we have discretized the interval and replaced the differential equation by the Differential quadrature method based on Fourier expansion basis to obtain a system of ordinary differential equation (ODE) then we implement the numerical scheme by computer programing and perform numerical solution. Finally the validation of the present scheme is demonstrated by numerical example and compared with some existing numerical methods in literature. The method is analyzed for stability and convergence. It is found that the proposed numerical scheme produces a good result as compared to other researcher’s result and even generates a value at the nodes or mesh points that the results have not seen yet.

关键词： Differential Quadrature Method Fourier Expansion Coupled Viscous Coupled Viscous Burgers’ Equation Initial and Boundary Conditions

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