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A high order numerical method for Ito stochastic Volterra integral equations | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 4، شماره 1، مهر 2024، صفحه 175-193 اصل مقاله (307.65 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2024.80370.1138 | ||
| نویسندگان | ||
| Sadegh Amiri* 1؛ Yasin Behrouzi2 | ||
| 1Department of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, P. O. Box 13846-63113, Tehran, Iran | ||
| 2Department of Mathematics, University of Birjand, Birjand, Iran | ||
| چکیده | ||
| The main purpose of this paper is to propose a high order numerical method based on the finite difference methods for solving nonlinear Itˆo stochastic Volterra integral equations (SVIEs) of the second kind. To develop the method, a fourth-order implicit finite difference method and the explicit Milstein method are implemented for the discretization of non-stochastic and stochastic integral parts, respectively. To solve the original SVIEs, the proposed method has the deterministic fourth-order and strong stochastic first-order accuracy. The convergence analysis of the proposed method is proved. The finite difference method under consideration requires solving a 2×2 system of equations at each step for one-dimensional SVIE. Therefore, the proposed method is very simple to implement and does not require a lot of computational cost. Some numerical examples are prepared to indicate the verity and efficiency of the new method. Moreover, the comparative numerical results show that this method is more accurate than those existing methods given in the literature. | ||
| کلیدواژهها | ||
| finite difference؛ Itˆo stochastic Volterra integral equations؛ fourth order | ||
| مراجع | ||
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