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

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

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 s...

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Veröffentlicht in:Numerical methods for partial differential equations 2021-05, Vol.37 (3), p.2730-2741
1. Verfasser: Günay Akdemir, Hande
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Differential equations
Mathematical analysis
Numerical methods
Ordinary differential equations
Runge-Kutta method
scalar noise
stochastic Runge–Kutta methods
Stratonovich stochastic differential equations
strong order of convergence
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Zusammenfassung: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.
ISSN:0749-159X
1098-2426
DOI:10.1002/num.22769