2
Malayer University, Faculty of Mathematical Sciences, Malayer, Iran
10.22080/cjms.2026.31111.1811
Abstract
In many modeling that occurs in various disciplines, including physics and biological mathematics, the stochastic factor is used to increase the accuracy of the model and make it more consistent with the reality of the phenomena. One of the equations in this family is the linear or nonlinear stochastic It\^{o}-Volterra integral equations (SIVIEs). This study investigated a method based on the operational matrix from linear cardinal B-spline functions by means of the Simpson's rule for a family of the linear or nonlinear SIVIEs due to the Brownian motion. To this end, we have created matrix forms for the Volterra integral as well as the stochastic It\^{o}-integral. Then we obtained the operational matrix of product, which we found to be not particularly computationally complex. By stating several theorems, we show that the method is convergent, and as a consequence of these theorems, we prove that the order of convergence of this method is $\mathbb{O}(\dfrac{1}{2^{2I}})$. Finally, by presenting several examples and comparing numerical results with other existing methods, the efficiency and high accuracy of the method were evaluated and some convergence verification notes for different values of $I$ to confirm the theoretical rates are demonstrated.
Moradpour, P. , Sayevand, K. , & Masti, I. (2026). Operational matrix approach based on linear cardinal B-splines for stochastic It\^{o} - Volterra integral equations. Caspian Journal of Mathematical Sciences, 15(2), 434-466. doi: 10.22080/cjms.2026.31111.1811
MLA
Payam Moradpour; Khosro Sayevand; Iman Masti. "Operational matrix approach based on linear cardinal B-splines for stochastic It\^{o} - Volterra integral equations", Caspian Journal of Mathematical Sciences, 15, 2, 2026, 434-466. doi: 10.22080/cjms.2026.31111.1811
HARVARD
Moradpour, P., Sayevand, K., Masti, I. (2026). 'Operational matrix approach based on linear cardinal B-splines for stochastic It\^{o} - Volterra integral equations', Caspian Journal of Mathematical Sciences, 15(2), pp. 434-466. doi: 10.22080/cjms.2026.31111.1811
CHICAGO
P. Moradpour , K. Sayevand and I. Masti, "Operational matrix approach based on linear cardinal B-splines for stochastic It\^{o} - Volterra integral equations," Caspian Journal of Mathematical Sciences, 15 2 (2026): 434-466, doi: 10.22080/cjms.2026.31111.1811
VANCOUVER
Moradpour, P., Sayevand, K., Masti, I. Operational matrix approach based on linear cardinal B-splines for stochastic It\^{o} - Volterra integral equations. Caspian Journal of Mathematical Sciences, 2026; 15(2): 434-466. doi: 10.22080/cjms.2026.31111.1811
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