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)

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 languageEnglish
Pages (from-to)1423-1430
Number of pages8
JournalApplied Mathematics and Computation
Volume181
Issue number2
DOIs
Publication statusPublished - Oct 15 2006

Fingerprint

Parabolic Partial Differential Equations
Nonlinear Partial Differential Equations
Partial differential equations
Boundary conditions
Mesh
Linear Diffusion
Unconditionally Stable
Nonlinear Parabolic Equations
Implicit Method
Diffusion equation
Dirichlet Boundary Conditions
Difference Method
Parabolic Equation
Linear equation
Singularity
Grid
Evaluation
Demonstrate

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

A new stable variable mesh method for 1-D non-linear parabolic partial differential equations. / Arora, Urvashi; Karaa, Samir; Mohanty, R. K.

In: Applied Mathematics and Computation, Vol. 181, No. 2, 15.10.2006, p. 1423-1430.

Research output: Contribution to journalArticle

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