We have established a uniform error bound for the Euler approximation to the solution process of the Stochastic Funtional Differential Equation (S.F.D.E.) (1.11) over the entire time span in this chapter. We discovered the upper bound for the difference between the actual solution process and its Euler approximation by computing the difference between the actual solution process and its Euler approximation. The reliance of this difference on the starting data has also been investigated. We've also shown that the solution process's Euler approximation has a significant convergence order.
Author(S) Details
Tagelsir A. Ahmed
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Khartoum, Sudan.
J. A. van Casteren
Department of Mathematics and Computer Science, University of Antwerp (UA), Middelheimlaan 1, 2020 Antwerp, Belgium.
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