On the Convergence of a One-step Method for the Numerical Solution of an Ordinary Differential Inclusion

Abstract

The approximation of the initial-value problem for the diferential inclusion $−dydt+f(t,y(t))∈β(y(t))$ by the one-step method $−(Yn−Ym−1h)+f(tn+θ,Ym+θ)∈β(Ym+θ)$ is considered. The multivalued mapping β is assumed to be maximal monotone. A convergence result and an error bound are established. An interative method for solving the discrete problem is given. Some examples are considered.