the purpose of this study is to present an approximate numerical method for solving high order linear fredholm-volterra integro-differential equations in terms of rational chebyshev functions under the mixed conditions. the method is based on the approximation by the truncated rational chebyshev series. finally, the effectiveness of the method is illustrated in several numerical examples. the p...

Here a posteriori error estimate for the numerical solution of nonlinear Voltena- Hammerstein equations is given. We present an error upper bound for nonlinear Voltena-Hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of Brunner for these problems (the implicitly linear collocation method)...

This manuscript presents Hyers-Ulam stability and Hyers--Ulam--Rassias stability results of non-linear Volterra integro--delay dynamic system on time scales with fractional integrable impulses. Picard fixed point theorem  is used for obtaining  existence and uniqueness of solutions. By means of   abstract Gr"{o}nwall lemma, Gr"{o}nwall's inequality on time scales, we establish  Hyers-Ulam stabi...

The purpose of this study is to present an approximate numerical method for solving high order linear Fredholm-Volterra integro-differential equations in terms of rational Chebyshev functions under the mixed conditions. The method is based on the approximation by the truncated rational Chebyshev series. Finally, the effectiveness of the method is illustrated in several numerical examples. The p...

In this paper, the Adomian decomposition method and Modified Technique are successfully applied to find approximate solutions of fuzzy system Volterra integro-differential equations. The obtained have been improved by using iteration integral equation numerical solution with Simpson rule Trapezoidal rule. These proposed methods gave excellent results close exact solution. show that present is v...

In this paper stability inequalities for the linear nonhomogeneous Volterra delay integro-differential equation (VDIDE) is being established. The particular problems are encountered to show applicability of method and confirm predicted theoretical analysis.

In this paper a higher-order numerical solution of a non-linear Volterra integro-differential equation is discussed. Example of this question has been solved numerically using the Runge-Kutta-Verner method for Ordinary Differential Equation (ODE) part and Newton-Cotes formulas for integral parts.

in this paper, a novel hybrid method based on learning algorithmof fuzzy neural network and newton-cotesmethods with positive coefficient for the solution of linear fredholm integro-differential equation of the second kindwith fuzzy initial value is presented. here neural network isconsidered as a part of large field called neural computing orsoft computing. we propose alearning algorithm from ...

The time-dependent Maxwell system is supplemented with the constitutive relations of linear bianisotropic media and is treated as a neutral integro-differential equation in a Hilbert space. By using the theory of abstract Volterra equations and strongly continuous semigroups we obtain general well-posedness results for the corresponding mathematical problem.