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An explicit order 2 scheme for the strong approximation of Stratonovich stochastic differential equations with scalar noise
Author(s) -
Günay Akdemir Hande
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22769
Subject(s) - mathematics , scalar (mathematics) , stochastic differential equation , runge–kutta methods , ordinary differential equation , stochastic partial differential equation , order (exchange) , stochastic calculus , class (philosophy) , mathematical analysis , differential equation , computer science , geometry , finance , economics , artificial intelligence
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.