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.
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Communicated by A. Miele
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Chang, R.Y., Wang, M.L. Shifted Legendre direct method for variational problems. J Optim Theory Appl 39, 299–307 (1983). https://doi.org/10.1007/BF00934535
- Shifted Legendre polynomials
- operational matrix
- variational problems