Solving the equation - uxx - ∈Uyy = f(x, y, u) by an O(h4) finite difference method

E. Lungu, T. Motsumi, Tadeusz Styś

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Abstract

The semi-linear equation - uxx - ∈uyy = f(x,y,u) with Dirichlet boundary conditions is solved by an O(h4) finite difference method, which has local truncation error O(h2) at the mesh points neighboring the boundary and O(h4) at most interior mesh points. It is proved that the finite difference method is O(h4) uniformly convergent as h → 0. The method is considered in the form of a system of algebraic equations with a nine diagonal sparse matrix. The system of algebraic equations is solved by an implicit iterative method combined with Gauss elimination. A Mathematica module is designed for the purpose of testing and using the method. To illustrate the method, the equation of twisting a springy rod is solved.

Original languageEnglish
Pages (from-to)395-407
Number of pages13
JournalNumerical Methods for Partial Differential Equations
Volume16
Issue number4
Publication statusPublished - Jul 2000

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics
  • Computational Mathematics

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