Boundary element methods are being applied with increasing frequency to time dependent problems, especially to boundary value problems for parabolic differential equations. Here we shall consider the heat equation as the prototype of such equations. Various types of integral equations arise when solving boundary value problems for the heat equation. An important one is the single layer heat pot...

‎‎‎in this paper‎, ‎we develop multi-step methods to solve a class of two-dimensional nonlinear volterra integral equations (2d-nvies) of the first kind‎. ‎here‎, ‎we convert a 2d-nvie of the first kind to a one-dimensional linear vie of the first kind and then we solve the resulted equation numerically by multi-step methods‎. ‎we also verify convergence and error analysis of the method‎. ‎at t...

Since the solution of a second-kind Volterra integral equation with weakly singular kernel has, in general, unbounded derivatives at the left endpoint of the interval of integration, its numerical solution by polynomial spline collocation on uniform meshes will lead to poor convergence rates. In this paper we investigate the convergence rates with respect to graded meshes, and we discuss the pr...

A method for stable numerical differentiation of noisy data is proposed. The method requires solving a Volterra integral equation of the second kind. This equation is solved analytically. In the examples considered its solution is computed analytically. Some numerical results of its application are presented. These examples show that the proposed method for stable numerical differentiation is n...

In this work we consider a nonlinear Volterra integral equation with weakly singular kernel. An asymptotic error expansion for the explicit Euler’s method is obtained and this allows the use of certain extrapolation procedures. The performance of the extrapolation method is illustrated by several numerical examples.

Abstract We study the Volterra integro-differential equation on time scales and provide sufficient conditions for boundness of all solutions considered equation. Using that result, we present exponential stability All results proved general scale include both integral discrete equations.

The integral equation method is widely used for solving many problems in mathematical physics and engineering. This article proposes a computational method for solving nonlinear Fredholm-Volterra integral equations. Several numerical methods for approximating the solution of linear and nonlinear integral equations and specially FredholmVolterra integral equations are known [1-10]. Also, BlockPu...