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Original Articles

Families of backward differentiation methods based on trigonometric polynomials

Pages 67-75 | Received 01 Jul 1985, Published online: 19 Mar 2007
 

Abstract

Backward differentiation methods based on trigonometric polynomials for the initial value problems whose solutions are known to be periodic are constructed. It is assumed that the frequency wcan be estimated in advance. The resulting methods depend on a parameter v = hw, where his the step size, and reduce to classical backward methods if v→0. Neta and Ford [6] constructed Nyström and generalized Milne-Simpson type methods. Those methods require the Jacobian matrix to have purely imaginary eigenvalues. The methods we construct here will not suffer of this deficiency.

C.R. Categories:

*Permanent address: Naval Postgraduate School, Department of Mathematms, Monlerey. CA 93943. U.S.A.

*Permanent address: Naval Postgraduate School, Department of Mathematms, Monlerey. CA 93943. U.S.A.

Notes

*Permanent address: Naval Postgraduate School, Department of Mathematms, Monlerey. CA 93943. U.S.A.

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