Diagonally drift-implicit Runge–Kutta methods of strong order one for stiff stochastic differential systems

Haghighi, Amir; Hosseini, Seyed Mohammad; Rößler, Andreas

doi:10.1016/j.cam.2015.02.036

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Approximation Of Stratonovich Stochastic Integrals1

Introduction1

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2024

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Cited by 9 publications

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“…We need to simulate the Stratonovich stochastic integrals J 1 , J 10 , J 101 which are defined by the following Equation (9). See [16] for details.…”

Section: Approximation Of Stratonovich Stochastic Integralsmentioning

confidence: 99%

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An explicit order 2 scheme for the strong approximation of Stratonovich stochastic differential equations with scalar noise

Akdemir

2021

Numerical Methods Partial

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A new class of stochastic Runge-Kutta (SRK) methods for the strong approximation of Stratonovich stochastic ordinary differential equations (SODEs) is presented. The proposed method is an alternative to the method of Xiao and Tang (Numer. Algor. 72: 259-296, 2016) and converges with order 2 in the strong sense. To validate the efficiency and to compare with some known methods, numerical simulations which involve generating Stratonovich stochastic integrals of level 3, are finally given.

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“…We need to simulate the Stratonovich stochastic integrals J 1 , J 10 , J 101 which are defined by the following Equation (9). See [16] for details.…”

Section: Approximation Of Stratonovich Stochastic Integralsmentioning

confidence: 99%

“…Burrage and Burrage [4] and Rössler [14] extended the idea of systematic calculation by using the colored rooted trees and B‐series. A great deal of work has been done on constructing SRK methods in the last decade; see, for instance [1, 6–9, 12, 13, 15, 17].…”

Section: Introductionmentioning

confidence: 99%