Split S-ROCK Methods for High-Dimensional Stochastic Differential Equations

We propose explicit stochastic Runge–Kutta (RK) methods for high-dimensional Itô stochastic differential equations. By providing a linear error analysis and utilizing a Strang splitting-type approach, we construct them on the basis of orthogonal Runge–Kutta–Chebyshev methods of order 2. Our methods...

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Bibliographic Details
Published in:Journal of scientific computing Vol. 97; no. 3; p. 62
Main Authors: Komori, Yoshio, Burrage, Kevin
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2023
Springer Nature B.V
Subjects:
Accuracy
Algorithms
Approximation
Chebyshev approximation
Computational Mathematics and Numerical Analysis
Differential equations
Eigenvalues
Error analysis
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical functions
Mathematics
Mathematics and Statistics
Methods
Numerical analysis
Ordinary differential equations
Random variables
Runge-Kutta method
Theoretical
65L05
65L06
60H10
Explicit method
Orthogonal Runge–Kutta–Chebyshev method
Itô stochastic differential equation
Stiffness
Weak second order approximation
Noncommutative noise
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary:We propose explicit stochastic Runge–Kutta (RK) methods for high-dimensional Itô stochastic differential equations. By providing a linear error analysis and utilizing a Strang splitting-type approach, we construct them on the basis of orthogonal Runge–Kutta–Chebyshev methods of order 2. Our methods are of weak order 2 and have high computational accuracy for relatively large time-step size, as well as good stability properties. In addition, we take stochastic exponential RK methods of weak order 2 as competitors, and deal with implementation issues on Krylov subspace projection techniques for them. We carry out numerical experiments on a variety of linear and nonlinear problems to check the computational performance of the methods. As a result, it is shown that the proposed methods can be very effective on high-dimensional problems whose drift term has eigenvalues lying near the negative real axis and whose diffusion term does not have very large noise.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-023-02354-8