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A novel optimization algorithm for solving two-point boundary value problems

A new algorithm for obtaining the numerical approximation to the solution of two-point boundary value problems based on the use of adaptive Differential Evolution (DE) algorithm is presented. The proposed algorithm might be considered as a variation of the finite difference method in the context that each of the derivatives is replaced by an appropriate difference quotients approximation. This novel approach possesses main advantage as compared to other exiting methods; it can be applied without any limitations on the nature of the problem, type of classification, and the number of mesh points. A test case that include different classes of such equations of different types to demonstrate the efficiency and simplicity of the algorithm is presented.