A-STABILITY OF RUNGE-KUTTA METHODS FOR SYSTEMS WITH ADDITIVE NOISE

被引：30

作者：

HERNANDEZ, DB

SPIGLER, R

机构：

[1] CIMAT,GUANAJUATO 36000,GUANAJUATO,MEXICO

[2] UNIV PADUA,DMMMSA,I-35131 PADUA,ITALY

来源：

BIT | 1992年 / 32卷 / 04期

关键词：

NUMERICAL STABILITY; RUNGE-KUTTA METHODS; IMPLICIT METHODS; STOCHASTIC DIFFERENTIAL EQUATIONS; STOCHASTIC STABILITY;

D O I：

10.1007/BF01994846

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Numerical stability of both explicit and implicit Runge-Kutta methods for solving ordinary differential equations with an additive noise term is studied. The concept of numerical stability of deterministic schemes is extended to the stochastic case, and a stochastic analogue of Dahlquist's A-stability is proposed. It is shown that the discretization of the drift term alone controls the A-stability of the whole scheme. The quantitative effect of implicitness upon A-stability is also investigated, and stability regions are given for a family of implicit Runge-Kutta methods with optimal order of convergence.

引用

页码：620 / 633

页数：14

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