An adaptive differential evolution algorithm for solving second-order dirichlet problems

A new adaptive Differential Evolution (DE) algorithm for finding approximate to the solutions of second-order Dirichlet problems is presented. The proposed adaptive algorithm reflected a variation of the finite difference scheme in the perspective that each of the derivatives are approximated by forward, backward, and central differences' quotients. The major advantage of the novel adaptive algorithm over other numerical methods; it has no limitations on the nature of the problem, type of classification, and the number of mesh points. A test cases that include different classes and types of Dirichlet problems to demonstrate the efficiency and simplicity of the algorithm are presented. The numerical results obtained show strong agreement with exact solutions, and demonstrate reliability and great accuracy of the method.