P. P. Paikaray - Department of Mathematics, College of Basic Science and Humanities, OUAT, Bhubaneswar, Odisha, 751003, India. S. Beuria - Department of Mathematics, College of Basic Science and Humanities, OUAT, Bhubaneswar, Odisha, 751003, India. N. Ch. Parida - Department of Mathematics, College of Basic Science and Humanities, OUAT, Bhubaneswar, Odisha, 751003, India.
In this paper, we propose a numerical approach for solving \(p\)-dimensional stochastic Volterra integral equations using the Walsh function approximation. The main goal is to transform integral equations into an algebraic system and solve this further to get an approximate solution to the integral equation. The convergence and error analysis of the proposed method are studied for integral equations having functions in the Lipschitz class. The computation of various examples for which analytical solutions are available shows that the proposed method is more accurate than the existing techniques for solving linear \(p\)-dimensional stochastic Volterra integral equations.
P. P. Paikaray, S. Beuria, N. Ch. Parida, Numerical approximation of \(p\)-dimensional stochastic Volterra integral equation using Walsh function, Journal of Mathematics and Computer Science, 31 (2023), no. 4, 448--460
Paikaray P. P., Beuria S., Parida N. Ch., Numerical approximation of \(p\)-dimensional stochastic Volterra integral equation using Walsh function. J Math Comput SCI-JM. (2023); 31(4):448--460
Paikaray, P. P., Beuria, S., Parida, N. Ch.. "Numerical approximation of \(p\)-dimensional stochastic Volterra integral equation using Walsh function." Journal of Mathematics and Computer Science, 31, no. 4 (2023): 448--460
