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- W2040540096 abstract "Let $alpha leqq a < b$ be real numbers and let $C([t_1 ,t_2 ] to E^n )$ denote the space of continuous functions on $[t_1 ,t_2 ]$ into $E^n $ (n-dimensional Euclidean space). We consider the Cauchy problem for Volterra functional differential equations: [y'(t) = F(y,t),quad ,t in [a,b];qquad ,y(t) = g(t),quad, t[alpha ,b].] Here, $F:C([alpha ,b] to E^n ]) times [a,b] to E^n $ is a Volterra functional, that is, $F(y,t)$ depends on t and on $y(s)$ for $s in [alpha ,t]$, but is independent of $y(s)$ for $s > t$; and $g in C([alpha ,a] to E^n )$ is a specified initial function. This problem includes as special cases the initial value problems for ordinary differential equations, retarded ordinary differential equations, and Volterra integro-differential equations. We develop two methods for numerically solving the Cauchy problem for Volterra functional equations; these methods are generalizations of the methods of Euler and Heun for ordinary differential equations. It is proved that these methods converge and a numerical example is given." @default.
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- W2040540096 title "The Numerical Solution of Volterra Functional Differential Equations by Euler’s Method" @default.
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- W2040540096 doi "https://doi.org/10.1137/0709012" @default.
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