论文信息 - Shifted Legendre direct method for variational problems

Shifted Legendre direct method for variational problems

The shifted Legendre polynomial series is employed to solve variational problems. The solution is carried out by using an operational matrix for integrating the shifted Legendre polynomial vector. Variational problems are reduced to solving algebraic equations. Two illustrative examples are given, and the computational results obtained by Legendre series direct method are compared with the exact solutions.

Maw-Ling Wang | R. Chang | R. Y. Chang | M. L. Wang

[1] A. Miele. Recent advances in gradient algorithms for optimal control problems , 1975 .

[2] A. V. Levy,et al. Summary and comparison of gradient-restoration algorithms for optimal control problems , 1972 .

[3] G. F. Newell,et al. The variational method in engineering , 1968 .

[4] A. E. Bryson,et al. A Steepest-Ascent Method for Solving Optimum Programming Problems , 1962 .

[5] I. S. Gradshteyn,et al. Table of Integrals, Series, and Products , 1976 .

[6] Bertram Ross,et al. Solved Problems: Gamma and Beta Functions, Legendre Polynomials, Bessel Functions , 1963 .

[7] C. Hwang,et al. Laguerre series direct method for variational problems , 1983 .

[8] C. F. Chen,et al. A walsh series direct method for solving variational problems , 1975 .

[9] Henry J. Kelley,et al. Gradient Theory of Optimal Flight Paths , 1960 .

[10] A. Miele,et al. Sequential gradient-restoration algorithm for optimal control problems , 1970 .

[11] J. Villadsen,et al. Solution of differential equation models by polynomial approximation , 1978 .