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- W1537563361 abstract "In this paper we solve by exponentially‐fitted difference scheme a singularly perturbed nonlinear two‐dimensional convection‐diffusion equation. To find the solution of the nonlinear algebraic system we use both Newton and Picard methods. We propose a new version of the two‐grid method with an exponential interpolation. In the first step the nonlinear differential problem is solved on a “coarse” grid of size H. In the second step, the problem is linearized around an appropriate interpolant of the computed solution on the first step and the linear problem then is solved on a fine grid of size h<<H. It is shown that the algorithms achieve optimal accuracy as long as the mesh size satisfies h = O(H2m), m = 1, 2,... , where m is the number of the Newton (Picard) iteration for the difference scheme. The convergence of the discrete solutions is always e—uniformly. We count the number of the arithmetical operations to illustrate the computational cost of the algorithms." @default.
- W1537563361 created "2016-06-24" @default.
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- W1537563361 date "2009-01-01" @default.
- W1537563361 modified "2023-09-26" @default.
- W1537563361 title "Two-grid Algorithms for The Solution of 2D Semilinear Singularly-perturbed Convection-diffusion Equations Using an Exponential Finite Difference Scheme" @default.
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- W1537563361 doi "https://doi.org/10.1063/1.3265351" @default.
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