in this paper, we present legendre wavelet method to obtain numerical solution of a singular integro-differential equation. the singularity is assumed to be of the cauchy type. the numerical results obtained by the present method compare favorably with those obtained by various galerkin methods earlier in the literature.

in this paper, a numerical solution for a system of linear fredholm integro-differential equations by means of the sinc method is considered. this approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. the exponential convergence rate $o(e^{-k sqrt{n}})$ of the method is proved. the analytical results are illustrated with numerical examp...

Infinite horizon backward stochastic Volterra integral equations (BSVIEs for short) are investigated. We prove the existence and uniqueness of adapted M-solution in a weighted $L^2$-space. Furthermore, we extend some important known results finite BSVIEs to infinite setting. provide variation constant formula class linear duality principle between (forward) equation (SVIE an BSVIE As applicatio...

in this article we have considered a non-standard finite difference method for the solution of second order  fredholm integro differential equation type initial value problems. the non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the fredholm integro-differential equation into a system of equations. we have also developed a numerical met...

‎in this paper‎, ‎we construct a new iterative method for solving nonlinear volterra integral equation of second kind‎, ‎by approximating the legendre polynomial basis‎. ‎error analysis is worked using banach fixed point theorem‎. ‎we compute the approximate solution without using numerical method‎. ‎finally‎, ‎some examples are given to compare the results with some of the existing methods‎.

The stability in L norm is considered for the Ritz Volterra projection and some applications are presented in this paper As a result point wise error estimates are established for the nite ele ment approximation for the parabolic integro di erential equation Sobolev equations and a di usion equation with non local boundary value problem This work is supported in part by NSERC CANADA Journal of ...

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 we consider a risk model with two classes of insurance risks in the presence of a multi-layer dividend startegy. We assume that the two claim counting processes are, respectively, Poisson and Sparre Andersen with generalized Erlang(2) claim inter-arrival times. We derive an integro-differential equation system for the Gerber-Shiu functions for surplus-dependent premium rates and a...