An O(k2 + kh2 + h4) arithmetic average discretization for the solution of 1-D nonlinear parabolic equations

R. K. Mohanty, Samir Karaa, Urvashi Arora

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

This article develops a new two-level three-point implicit finite difference scheme of order 2 in time and 4 in space based on arithmetic average discretization for the solution of nonlinear parabolic equation ε u xx = f(x, t, u, ux, ut), 0 <1 <1, t > 0 subject to appropriate initial and Dirichlet boundary conditions, where ε > 0 is a small positive constant. We also propose a new explicit difference scheme of order 2 in time and 4 in space for the estimates of (∂u/∂x). The main objective is the proposed formulas are directly applicable to both singular and nonsingular problems. We do not require any fictitious points outside the solution region and any special technique to handle the singular problems. Stability analysis of a model problem is discussed. Numerical results are provided to validate the usefulness of the proposed formulas.

Original languageEnglish
Pages (from-to)640-651
Number of pages12
JournalNumerical Methods for Partial Differential Equations
Volume23
Issue number3
DOIs
Publication statusPublished - May 2007

Fingerprint

Nonlinear Parabolic Equations
Discretization
Boundary conditions
Singular Problems
Explicit Scheme
Difference Scheme
Finite Difference Scheme
Dirichlet Boundary Conditions
Stability Analysis
Numerical Results
Estimate
Model

Keywords

  • Arithmetic average discretization
  • Burgers' equation
  • Diffusion-convection equation
  • Implicit scheme
  • Nonlinear parabolic equation
  • RMS errors
  • Singular problem

ASJC Scopus subject areas

  • Applied Mathematics
  • Analysis
  • Computational Mathematics

Cite this

An O(k2 + kh2 + h4) arithmetic average discretization for the solution of 1-D nonlinear parabolic equations. / Mohanty, R. K.; Karaa, Samir; Arora, Urvashi.

In: Numerical Methods for Partial Differential Equations, Vol. 23, No. 3, 05.2007, p. 640-651.

Research output: Contribution to journalArticle

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