A Numerical Algorithm for Ambrosetti-Prodi Type Operators
arXiv:1103.6260h-index: 18
Originality Synthesis-oriented
AI Analysis
It provides a numerical approach for a specific class of PDEs, but the results are incremental and limited to theoretical examples.
The paper presents a numerical algorithm for solving a class of semilinear elliptic equations with bounded nonlinearities, using finite elements and a global Lyapunov-Schmidt decomposition. The method is demonstrated on test problems, showing convergence and efficiency.
We consider the numerical solution of the equation - Δu - f(u) = g, for the unknown u satisfying Dirichlet conditions in a bounded domain. The nonlinearity f has bounded, continuous derivative. The algorithm uses the finite element method combined with a global Lyapunov-Schmidt decomposition.