Keywords: Volterra integro-differential equations Multistep collocation Superconvergence Stability a b s t r a c t Multistep collocation methods for Volterra integro-differential equations are derived and analyzed. They increase the order of convergence of classical one-step collocation methods, at the same computational cost. The numerical stability analysis is carried out and classes of A 0-s...

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...

in this paper, the variational iteration method for solving nth-order fuzzy integro differential equations (nth-fide) is proposed. in fact the problem is changed to the system of ordinary fuzzy integro-differential equations and then fuzzy solution of nth-fide is obtained. some examples show the efficiency of the proposed method.

We consider, in an abstract setting, an instance of the Coleman-Gurtin model for heat conduction with memory, that is, the Volterra integro-differential equation ∂tu(t)− β∆u(t)− ∫ t 0 k(s)∆u(t− s)ds = 0. We establish new results for the exponential and polynomial decay of solutions, by means of conditions on the convolution kernel which are weaker than the classical differential inequalities.

The paper presents the foundations of theory linear fractional Volterra integro-differential equations convolution type in Banach spaces. It is established that existence a resolvent operator for such equivalent to well-posedness formulation initial problem them. Within framework this approach, theorem Hille–Yosida proved.

in this letter, the numerical scheme of nonlinear volterra-fredholm integro-differential equations is proposed in a reproducing kernel hilbert space (rkhs). the method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satis ed. the nonlinear terms are replaced by its taylor series. in this technique, the nonlinear volterra-fredholm integr...

In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds t...