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M. A. Celia, T. F. Russell, I. Herrera and R. E. Ewing, “An Eulerian-Langrangian Localized Adjoint Method for the Advection-Diffusion Equation,” Advances in Water Resources, Vol. 13, No. 4, 1990, pp. 187-206. doi:10.1016/0309-1708(90)90041-2

has been cited by the following article:

• TITLE: Exponential B-Spline Solution of Convection-Diffusion Equations

  AUTHORS: Reza Mohammadi

  KEYWORDS: Exponential B-Spline; Convection-Diffusion Equation; Collocation; Crank-Nicolson Formulation;

  JOURNAL NAME: Applied Mathematics, Vol.4 No.6, June 17, 2013

  ABSTRACT: We present an exponential B-spline collocation method for solving convection-diffusion equation with Dirichlet’s type boundary conditions. The method is based on the Crank-Nicolson formulation for time integration and exponential B-spline functions for space integration. Using the Von Neumann method, the proposed method is shown to be unconditionally stable. Numerical experiments have been conducted to demonstrate the accuracy of the current algorithm with relatively minimal computational effort. The results showed that use of the present approach in the simulation is very applicable for the solution of convection-diffusion equation. The current results are also seen to be more accurate than some results given in the literature. The proposed algorithm is seen to be very good alternatives to existing approaches for such physical applications.