---

Discontinuity, Nonlinearity, and Complexity 7(4) (2018) 397--401 | DOI:10.5890/DNC.2018.12.004

R. Zeghdane, A. Tocino

Department of Mathematics, University of Bordj Bou Arreridj, Algeria

Department of Mathematics, University of Salamanca, Spain

Download Full Text PDF

 

Abstract

Deterministic predictor-corrector schemes are used mainly because of their numerical stability which they inherit from implicit counterparts of their corrector schemes. In principle these advantages carry over to the stochastic case. In this paper a complete study for the linear MS-stability of the oneparameter family of weak order 1.0 predictor-corrector Taylor schemes for scalar stochastic differential equations is given. Figures of the MS-stability regions that confirm the theoretical results are shown. It is also shown that mean- square A-stability is recovered if the parameter is increased.

References

1. [1]	Arnold, L. (1974), Stochastic Differential Equations, Wiley, New York.

2. [2]	Higham, D.J. (2000), Mean-square and asymptotic stability of the stochastic theta method, SIAM J. Numer. Anal., 38, 753-769.

3. [3]	Higham, D.J. (2000), A-stability and stochastic mean-square stability, BIT , 40, 404-409.

4. [4]	Kloeden, P.E. and Platen, E. (1992), Numerical solution of stochastic differential equations, Springer, Berlin.

5. [5]	Saito, Y. and Mitsui, T. (1996), Stability analysis of numerical schemes for stochastic differential equations, SIAM J. Numer. Anal., 33, 2254-2267.

6. [6]	Saito, Y. andMitsui, T. (2002),Mean-square stability of numerical schemes for stochastic differential systems, Vietnam J. Math., 30, 551-560.

7. [7]	Schurz, H. (1996), Asymptotical mean square stability of an equilibrium point of some linear numerical solutions with multiplicative noise, Stoch. Anal. Appl. , 14, 313-354.