A new stable variable mesh method for 1-D non-linear parabolic partial differential equations

Urvashi Arora, Samir Karaa, R. K. Mohanty

Research output: Contribution to journalArticle

7 Citations (Scopus)


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 languageEnglish
Pages (from-to)1423-1430
Number of pages8
JournalApplied Mathematics and Computation
Issue number2
Publication statusPublished - Oct 15 2006



  • Arithmetic average discretization
  • Burgers' equation
  • Diffusion equation
  • Finite difference method
  • Implicit method
  • Variable mesh

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

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