An approximate solution of a differential inclusion with maximal monotone operator

Abstract

The theory of differential inclusions has played a central role in many areas as biological systems, physical problems and population dynamics. The principle aim of our work is to compute explicitly the discrete approximate solution of a differential inclusion including a maximal monotone operator. Also we present a numerical application of our results for showing how to compute the discrete approximate solution of its corresponding differential inclusion.

Finding a Zero of the Sums of Three Maximal Monotone Operators

“…The second section presents a new method is given to determine set of solution of this problem. The technique used in this work can be applied in the future to generalize and develop the results obtained in [1,10,11].…”

Discrete Approximate Solution of Differential Inclusion with Normal Cone and Prox-Regular Set.

“…In our work, we will present a numerical method for calculating the approximate solution of a differential inclusion with normal cone for prox-regular sets, this problem has been studied extensively see, [18], [19], [17], for existence and uniqueness of the solutions see, [11], [12], [3], [9] and also gave some properties and theories that help us reach the proof of the proposed convergence on our side. We use also the same method (Discrete approximation solution), see, [14], [15], [7], [22], [20], [4], knowing that these methods were applied to the differential inclusion ẋ(t) ∈ F (x(t)) a.e t ∈ [0, T ] , x (0) = x 0 that was studied by Mordukhovich, see, [13] and also applied to the differential inclusion ẋ(t) ∈ −N C (x(t)) a.e t ∈ [0, T ] , x (0) = x 0 see, [16]. In this paper we will study the following problem.…”

“…[4] Let b be a postive real number and f (•), g(•) two functions in L 1 ([0, b], R) such that the function g(•) is positive on [0,b], and let w be an absolutely continuous function from [0, b…”

A method for finding a zero of the sum of maximal monotone operators

“…where > 0 is the proximal parameter. The technique used in this work can be applied in the future to generalize and develop the results obtained in [2,3,8].…”