Using our previous work on reflectionless analytic difference operators and a nonlocal Toda equation, we introduce analytic versions of the Volterra and Kac-van Moerbeke lattice equations. The real-valued N -soliton solutions to our nonlocal equations correspond to self-adjoint reflectionless analytic difference operators with N bound states. A suitable scaling limit gives rise to the N -solito...

...................................................................................................................3 Research Project Background.............................................................................4 -Predator-Prey Interaction -Natural Selection and Coevolution -The Test Case: Canadian Lynx and Snowshoe Hare Laying a Foundation in Differential Equations......................

The method of generalized quasilinearization technique when is applied to the nonlinear integrodifferential equations of Volterra type, gives two sequences of linear integro-differential equations with solutions monotonically and quadratically convergent to the solution of nonlinear equation. In this paper we employ step-by-step collocation method to solve the linear equations numerically and t...

We develop a theoretical context in which to study the future-sequential regularization method developed by J. V. Beck for the Inverse Heat Conduction Problem. In the process, we generalize Beck’s ideas and view that method as one in a large class of regularization methods in which the solution of an ill-posed first-kind Volterra equation is seen to be the limit of a sequence of solutions of we...

in this paper, existence theorems for the fuzzy volterra-fredholm integral equations of mixed type (fvfiemt) involving fuzzy number valued mappings have been investigated. then, by using banach's contraction principle, sufficient conditions for the existence of a unique solution of fvfiemt are given. finally, illustrative examples are presented to validate the obtained results.

In this study, a fractional nonlinear mixed integro-differential equation (Fr-NMIDE) is presented and has general discontinuous kernel based on position time space. Conditions of the existence uniqueness solution provided through principal form integral equation, Banach fixed point theorem. After applying properties integral, Fr-NMIDE conformed to Volterra–Hammerstein (V-HIE) second kind, with ...

We consider a nonlinear Volterra integro-differential equation with periodic solution, a special case of which has been used in modeling hematopoiesis dynamics. Some analytical results concerning existence and uniqueness of a positive periodic solution are presented together with some numerical results based on the reformulation of the equation as a system of ODEs and also from its direct solut...