Nonstandard finite difference equations for ODEs and 1-D PDEs based on piecewise linearization
The authors construct nonstandard finite difference schemes for nonlinear ordinary and one-dimensional partial differential equations. The method of construction consists in employing piecewise linearization, which reduces the nonlinear equation to a piecewise one. The latter can be integrated analytically subject to appropriate continuity conditions for both its solution and the first-order derivative of the solution in order to get three-point nonlinear difference schemes, the solution of which provides the nodal values of the approximate solution. The solution of the nonlinear difference schemes requires the use of iterative techniques.
scientific article; zbMATH DE number 1183156
scientific article