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.
|Number of pages
|Numerical Methods for Partial Differential Equations
|Published - Jul 2000
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Computational Mathematics