A linearized difference scheme for semilinear parabolic equations with nonlinear absorbing boundary conditions

Zhi Zhong Sun*, Xiaonan WU, Jiwei Zhang, Desheng Wang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

6 Citations (Scopus)

Abstract

A novel three level linearized difference scheme is proposed for the semilinear parabolic equation with nonlinear absorbing boundary conditions. The solution of this problem will blow up in finite time. Hence this difference scheme is coupled with an adaptive time step size, i.e., when the solution tends to infinity, the time step size will be smaller and smaller. Furthermore, the solvability, stability and convergence of the difference scheme are proved by the energy method. Numerical experiments are also given to demonstrate the theoretical second order convergence both in time and in space in L -norm.

Original languageEnglish
Pages (from-to)5187-5201
Number of pages15
JournalApplied Mathematics and Computation
Volume218
Issue number9
DOIs
Publication statusPublished - 1 Jan 2012

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Convergence
  • Finite difference scheme
  • Nonlinear local absorbing boundary conditions
  • Nonuniform time step
  • Parabolic problems in unbounded domains
  • Solvability
  • Stability
  • Unified approach

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