The Use of Richardson Extrapolation in One-Step Methods with Variable Step Size

The Use of Richardson Extrapolation in One-Step Methods with Variable Step Size*

1. Introduction. One of the objections to the use of a one-step method to integrate a system of ordinary differential equations is that an estimate of the accumulated truncation error is difficult to make. If an attempt is made at appraising the truncation error, it is usually confined to an approximate evaluation of the local truncation error. A scheme for estimating the local truncation error...

Mean-square Convergence of Stochastic Multi-step Methods with Variable Step-size

Abstract. We study mean-square consistency, stability in the mean-square sense and meansquare convergence of drift-implicit linear multi-step methods with variable step-size for the approximation of the solution of Itô stochastic differential equations. We obtain conditions that depend on the step-size ratios and that ensure mean-square convergence for the special case of adaptive two-step Maru...

The Wavelet Transform-Domain LMS Adaptive Filter Algorithm with Variable Step-Size

The wavelet transform-domain least-mean square (WTDLMS) algorithm uses the self-orthogonalizing technique to improve the convergence performance of LMS. In WTDLMS algorithm, the trade-off between the steady-state error and the convergence rate is obtained by the fixed step-size. In this paper, the WTDLMS adaptive algorithm with variable step-size (VSS) is established. The step-size in each subf...

Variable Step Size Destabilizes the St {

For fixed step-size h the Strrmer method is stable for the standard test equation y = co2y, co > O, if and only ifhco < 2. We show that for variable step size h~ there does not exist a (positive) limit on hco which ensures stability. Nor can we guarantee stability if, in addition, we limit the step size ratio h~/h,_ 1AMS(MOS) Subject Classifications: 65L20.

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