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Optimal control of nonlinear Volterra integral equations via Legendre polynomials. (English) Zbl 1275.49056
Summary: This paper contributes an efficient numerical approach for solving optimal control problems governed by nonlinear Volterra integral equations. The technique is based upon orthogonal Legendre polynomials. Theoretical analysis is given to support the method. In order to demonstrate the applicability, efficiency and accuracy of the proposed method, we examine two illustrative examples.

49M30 Other numerical methods in calculus of variations (MSC2010)
45D05 Volterra integral equations
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
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