Shifted Chebyshev direct method for solving variational problems

Abstract

Shifted Chebyshev polynomials for solving variational problems are given in this study. This technique reduces a variational problem to the solution of algebraic equations, and the computation is straightforward on a digital computer. Two illustrative examples are given. Only a small number of the shifted Chebyshev polynomials are needed to calculate the Chebyshev coefficients, and the result produced is very attractive and accurate.