In this research, the finite difference method is used to solve initial value problem of linear first order Volterra-Fredholm integro-differential equations with singularity. By using implicit rules and composite numerical quadrature rules, scheme established on a Shishkin mesh. The stability convergence proposed are analyzed two examples solved display advantages presented technique.

Integro-differential equations arise in modeling various physical and engineering problems. Several numerical and analytical methods have been developed to solving such equations. We introduce the OHAM (Optimal Homotopy Asymptotic Method) for solving nonlinear integro-differential equations. Several examples for solving integro-differential equations are presented to illustrate the reliability ...

The main purpose of this paper is to consider Adomian's decomposition method in non-linear Volterra integro-differential equations. The advantages of this method, compared with the recent numerical techniques (in particular the implicitly linear collocation methods) , and the convergence of Adomian's method applied to such nonlinear integro-differential equations are discussed. Finally, by ...

For scientists conducting research, fractional integral differential equation analysis is crucial. Therefore, in this study, we investigate utilizing a novel method called the decomposition method, which applicable to nonlinear Fredholm integro-differential equations. Then, apply approach five test problems for general derivative [Formula: see text] involving To best of our knowledge, are first...

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).we al...

The present paper is devoted to the development of a kind of spectral meshless radial point interpolation (SMRPI) technique in order to obtain a reliable approximate solution for buckling of nano-actuators subject to different nonlinear forces. To end this aim, a general type of the governing equation for nano-actuators, containing integro-differential terms and nonlinear forces is considered. ...

A collocation procedure is developed for the linear and nonlinear Fredholm and Volterra integro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. Numerical results are given t...

The scope of this study is to establish an effective approximation method for linear first order singularly perturbed Volterra-Fredholm integro-differential equations. finite difference scheme constructed on Shishkin mesh by using appropriate interpolating quadrature rules and exponential basis function. recommended second convergent in the discrete maximum norm. Numerical results illustrating ...