Block monotone iterative methods for numerical solutions of nonlinear elliptic equations
The problems considered are second-order nonlinear elliptic boundary-value problems on domains in the plane. The author shows that for the standard difference schemes there exists a preconditioning for which the corresponding block Picard, Jacobi, and Gauss-Seidel iterative methods converge monotonically. The efficacy of these methods is illustrated by an application to the logistic equation.
second-order nonlinear elliptic boundary value problems
scientific article; zbMATH DE number 839157