ANALYSIS OF A FAMILY OF CHEBYSHEV METHODS FOR Y'' = F(X, Y)

[摘要] Methods proposed by Panovsky and Richardson (this journal, 1988) are interpreted as a family of symmetric two-step hybrid methods. Each method is based on a polynomial interpolant of degree n for y'', for which the nodes are determined by the extrema of the Chebyshev polynomial of degree n. It is shown that the order of accuracy is n + 1 for odd n and n + 2 for even n, and expressions for the local error constants are given. The stability properties of each method are determined by the roots of a quadratic equation lambda2-2alpha(n)lambda + 1 = 0 where alpha(n)(nu2) is a rational approximation for cos nu. The intervals of periodicity, which are also intervals of absolute stability, are tabulated for n less-than-or-equal-to 10. Numerical examples provide comparisons with other methods.

[发布日期] 1992-12-09

[关键词] CHEBYSHEV METHODS;HYBRID METHODS;2ND-ORDER DIFFERENTIAL EQUATIONS;PERIODICITY INTERVALS