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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 장전수학회 Proceedings of the Jangjeon Mathematical Society Proceedings of the Jangjeon Mathematical Society Vol.22 No.1
- 발행연도
- 2019.1
- 수록면
- 119 - 128 (10page)
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Recently, there is growing interest in developing new numerical methods for stochastic di erential equations (SDEs), in order to improve the stability of approximation solution. There are many numerical methods have been constructed based on a Milstein scheme for SDEs. However, there exists very little results on the stability analysis of Milstein type methods for SDEs. This paper is concerned with mean-square (MS) stability of the semi-implicit theta Milstein methods and drifting split-step theta Milstein methods for nonlinear stochastic di erential equations. Under a coupled condition on the drifting and di usion coe cients, it is proved that, the methods with > 1 2 are unconditionally preserve the MS-stability of the SDEs. For 2 [0; 1 2 ], the methods are MS-stable for some small step-size. This work is di erent from the previous works such that we could get rid of the restrictions that existed on the step-size of two classes Milstein methods for a symptomatic mean-square stability of the non-linear stochastic di erential equations, under Local lipschitz condition. Numerical experiments are given to demonstrate the conclusions.
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참고문헌 (23)
참고문헌 신청
E. Buckwar / 2006 / Asymptotic mean-square stability of two-step methods for stochastic ordinary differential equations / BIT 46:261282
K. Burrage / 2001 / The composite Euler method for stiff stochastic differential equations / J. Comput. Appl. Math 131:407~426
K. Burrage / 2001 / Stiffly accurate RungeKutta methods for stiff stochastic differential equations / Comput. Phys. Commun 142:186~190
Mahmoud A. Eissaa / Split-Step Theta Milstein Methods for Stiff Stochastic Differential Equations / J. Comp. App. Math
M.A. Eissa / 2017 / Lobatto-Milstein Numerical Method in Application of Uncertainty Investment of Solar Power Projects / Energies 10(1):43
K. Burrage / 2001 / The composite Euler method for stiff stochastic differential equations / J. Comput. Appl. Math 131:407~426
K. Burrage / 2001 / Stiffly accurate RungeKutta methods for stiff stochastic differential equations / Comput. Phys. Commun 142:186~190
Mahmoud A. Eissaa / Split-Step Theta Milstein Methods for Stiff Stochastic Differential Equations / J. Comp. App. Math
M.A. Eissa / 2017 / Lobatto-Milstein Numerical Method in Application of Uncertainty Investment of Solar Power Projects / Energies 10(1):43
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