Keywords: Integro-differential equations Volterra equations Abel's integral equations Bernstein polynomials Singular volterra integral equations a b s t r a c t In this study, a new collocation method based on the Bernstein polynomials is introduced for the approximate solution of a class of linear Volterra integro-differential equations with weakly singular kernel. If the exact solution is pol...

In this paper, we studied the numerical solution of nonlinear weakly singular Volterra-Fredholm integral equations by using the product integration method. Also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear Volterra-Fredholm integral equations. The reliability and efficiency of the proposed scheme are...

In this work we consider a certain class of Volterra integral equations possessing an infinite set of solutions. We investigate the application of Euler’s method together with the use of extrapolation procedures. Several examples are considered illustrating our results as well as the use of graded meshes and the application of higher order methods. keywords Volterra integral equations; weakly s...

Volterra integral equations arise in many problems pertaining to mathematical physics like heat conduction problems. Several numerical methods for approximating the solution of Volterra integral equations are known [1-10]. This paper is focused on the solution of Volterra integral equations of the second kind with weakly singular kernel via Haar function by taking advantage of the nice properti...

stefan problem with kinetics is reduced to a system of nonlinear volterra integral equations of second kind and newton's method is applied to linearize it. product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. an example is provided to illustrated the applicability of the method.

Some existence and uniqueness theorems are established for weakly singular Volterra and Fredholm-Volterra integral equations in C[a, b]. Our method is based on fixed point theorems which are applied to the iterated operator and we apply the fiber Picard operator theorem to establish differentiability with respect to parameter. This method can be applied only for linear equations because otherwi...

‎A natural algorithm with an optimal order of convergence is proposed for numerical solution of a class of cordial weakly singular Volterra integral equations‎. ‎The equations of this class appear in heat conduction problems with mixed boundary conditions‎. ‎The algorithm is based on a representation of the solution and compound Gaussian quadrature rules with graded meshes‎. ‎A comparative stud...

In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad ‎et al., ‎‎[K. Maleknejad ‎and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, ‎Appl. Math. Comput.‎ (2005)]‎ to gain...

In this work we are concerned with the numerical solution of a nonlinear weakly singular Volterra integral equation with a nonsmooth solution. We investigate the application of product integration methods and a detailed analysis of the Trapezoidal method is given. In order to improve the numerical results we consider extrapolation procedures and collocation methods based on graded meshes. Sever...