An explicit two-stage truncated Runge–Kutta method for nonlinear stochastic differential equations

Haghighi, Amir

doi:10.1007/s40096-023-00508-1

Cited by 2 publications

(1 citation statement)

References 31 publications

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“…Moreover, Hu et al [22] studied the convergence rates and stability of the truncated EM method. The idea of the truncated EM method [20], which works by truncating the drift and diffusion coefficients of the SDEs in the EM method, was extended to the Milstein method [23], the split-step method [24], the Runge-Kutta method [25], nonautonomous SDEs [26], and to SDEs with Hölder continuous diffusion coefficients [27,28].…”

Section: Introductionmentioning

confidence: 99%

A split-step Euler-Maruyama based method with partial truncation coefficients for nonlinear SDEs

Haghighi

2024

Preprint

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The main objective of this paper is to develop and analyze a numerical method for the strong approximation of solutions to highly nonlinear stiff It\^{o} stochastic differential equations (SDEs). In this method, we first divide the coefficients of the SDEs into linear and nonlinear parts. Then, in two fully explicit recursive phases, we apply the appropriate truncation transformation only to the nonlinear parts of the coefficients of the SDEs at each step. Theoretical aspects are introduced to establish the $L^q$-convergence theory of the new method in the finite time interval $[0,T]$. The stability and boundedness properties of the solutions generated by the new method are also investigated. An important contribution is that the region of MS-stability of the new method includes the region of MS-stability of the partially truncated method proposed by Yang et al. (2022). Moreover, we show that the proposed method preserves the exponential MS-stability and the asymptotic boundedness of the SDEs. Finally, numerical experiments are performed to compare the efficiency of this method with an existing explicit method developed for nonlinear SDEs. MSC Classification: 65C30 , 65L07 , 65L04

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Section: Introductionmentioning

confidence: 99%

A split-step Euler-Maruyama based method with partial truncation coefficients for nonlinear SDEs

Haghighi

2024

Preprint

Self Cite

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Mean-square convergence of an explicit derivative-free truncated method for nonlinear SDEs covering the non-commutative noise case

Haghighi

2025

Journal of Computational and Applied Mathematics

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An explicit two-stage truncated Runge–Kutta method for nonlinear stochastic differential equations

Cited by 2 publications

References 31 publications

A split-step Euler-Maruyama based method with partial truncation coefficients for nonlinear SDEs

A split-step Euler-Maruyama based method with partial truncation coefficients for nonlinear SDEs

Mean-square convergence of an explicit derivative-free truncated method for nonlinear SDEs covering the non-commutative noise case

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