Improved rectangular method on stochastic Volterra equations

• Published in: Journal of computational and applied mathematics Vol. 235; no. 8; pp. 2492 - 2501
• Main Authors: Wen, C.H., Zhang, T.S.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 15-02-2011; Elsevier
• Subjects: Exact sciences and technology; Itô–Taylor expansion; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical schemes; Rectangular methods; Sciences and techniques of general use; Stochastic Volterra equations; 65C20; 37M99; 60H20; Rectangular methods; Itô–Taylor expansion; Numerical schemes; Stochastic Volterra equations; Error estimation; Numerical method; Stochastic method; Convergence; Exact solution; Numerical analysis; Applied mathematics; Numerical solution; Itô-Taylor expansion; Volterra equation; Volterra integral equations; Stochastic equation
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2010.11.002

An improved version of rectangular method (IRM) is introduced in this paper to numerically solve the stochastic Volterra equation (SVE). We focus on studying the order of error between the numerical and exact solutions, which is improved to
O
(
h
)
. Furthermore, an explicit form of the IRM scheme is introduced and its convergence is established. A numerical example has also been presented to show the feasibility of the methods.