Conjugate Gradient Method for the Solution of Optimal Control Problems Governed by Weakly Singular Volterra Integral Equations with the Use of the Collocation Method

Seminar paper from the year 2015 in the subject Mathematics - Applied Mathematics, grade: A, language: English, abstract: In this research, a novel method to approximate the solution of optimal control problems governed by Volterra integral equations of weakly singular types is proposed. The method introduced here is the conjugate gradient method with a discretization of the problem based on the collocation approach on graded mesh points for non linear Volterra integral equations with singular kernels. Necessary and sufficient optimality conditions for optimal control problems are also discussed. Some examples are presented to demonstrate the efficiency of the method.