Approximation of the solution of certain nonlinear ODEs with linear complexity
This paper deals with a finite difference method for the approximation of semilinear elliptic problems in one dimension subject to nonlinear Neumann boundary conditions. The main result provides an algorithm which computes an \(\varepsilon-\)approximation of a positive solution for the semilinear problem. Such an algorithm relies on the homotopy continuation method. It is also proved that the cost of the algorithm is linear in terms of the number of nodes involved in the discretization.
scientific article; zbMATH DE number 5669159
scientific article