Abstract
A numerical method for solving linear two-point boundary-value problems with time varying coefficients is presented in this paper. The method is based upon constructing the Nth degree polynomial interpolation using Legendre-Gauss-Lobatto nodes to approximate the solution of linear two-point value problems with time-varying coefficients. The method can be applied to obtain the optimal control of linear time-varying systems subject to a quadratic cost criteria. The two-point value problem is thereby transformed into a linear programming problem. The method is efficient and yields very accurate results. Illustrative examples are included to demonstrate the accuracy of the proposed method.
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