Optimal error estimate of an accurate second-order scheme for Volterra integrodifferential equations with tempered multi-term kernels

Polynomial spline collocation methods for second-order Volterra integrodifferential equations

where q : I → R, pi : I → R, and ki : D → R (i = 0,1) (with D := {(t,s) : 0 ≤ s ≤ t ≤ T}) are given functions and are assumed to be (at least) continuous in the respective domains. For more details of these equations, many other interesting methods for the approximated solution and stability procedures are available in earlier literatures [1, 3, 4, 5, 6, 7, 8, 11]. The above equation is usually...

An ELLAM Scheme for Multidimensional Advection-Reaction Equations and Its Optimal-Order Error Estimate

COLLOCATION METHOD FOR FREDHOLM-VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY KERNELS

In this paper it is shown that the use of‎ ‎uniform meshes leads to optimal convergence rates provided that‎ ‎the analytical solutions of a particular class of‎ ‎Fredholm-Volterra integral equations (FVIEs) are smooth‎.

Optimal Control for Stochastic Volterra Equations with Completely Monotone Kernels

In this paper, we study a class of stochastic optimal control problems, where the drift term of the equation has a linear growth on the control variable, the cost functional has a quadratic growth, and the control process belongs to the class of square integrable, adapted processes with no bound assumed on it. 2000 Mathematics Subject Classification: Primary 45D05 Secondary 93E20, 60H30

Ulam stabilities for nonlinear Volterra-Fredholm delay integrodifferential equations

In the present research paper we derive results about existence and uniqueness of solutions and Ulam--Hyers and Rassias stabilities of nonlinear Volterra--Fredholm delay integrodifferential equations. Pachpatte's inequality and Picard operator theory are the main tools that are used to obtain our main results. We concluded this work with applications of ob...