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Lejeune-Dirichlet, P. (1829) Sur la convergence des séries trigonométriques qui servent à représenter une fonction arbitraire entre des limites données. [On the Convergence of Trigonometric Series Which Serve to Represent an Arbitrary Function between Two Given Limits.] Journal für die reine und angewandte Mathematik, 4, 157-169. (In French)
https://doi.org/10.1515/crll.1829.4.157

has been cited by the following article:

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

  AUTHORS: Masho Jima, Alemayehu Shiferaw, Ali Tsegaye

  KEYWORDS: Differential Quadrature Method, Fourier Expansion, Coupled Viscous, Coupled Viscous Burgers’ Equation, Initial and Boundary Conditions

  JOURNAL NAME: Applied Mathematics, Vol.9 No.7, July 30, 2018

  ABSTRACT: 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.