Abstract
We propose a new stable variable mesh implicit difference method for the solution of non-linear parabolic equation uxx = φ{symbol}(x, t, u, ux, ut), 0 < x < 1, t > 0 subject to appropriate initial and Dirichlet boundary conditions prescribed. We require only (3 + 3)-spatial grid points and two evaluations of the function φ{symbol}. The proposed method is directly applicable to solve parabolic equation having a singularity at x = 0. The proposed method when applied to a linear diffusion equation is shown to be unconditionally stable. The numerical tests are performed to demonstrate the convergence of the proposed new method.
Original language | English |
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Pages (from-to) | 1423-1430 |
Number of pages | 8 |
Journal | Applied Mathematics and Computation |
Volume | 181 |
Issue number | 2 |
DOIs | |
Publication status | Published - Oct 15 2006 |
Keywords
- Arithmetic average discretization
- Burgers' equation
- Diffusion equation
- Finite difference method
- Implicit method
- Variable mesh
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics