In this research, we study the numerical solution of the singular Abel's equation of the
second kind. Solving this equation is challengeable, because of the nonlinear and …

In this paper, we present a numerical method for solving Volterra integral equations of the
second kind (VK2), first kind (VK1) and even singular type of these equations. The proposed …

This article discusses the development of a new algorithm, which is based on optimal
quadrature formulas for obtaining solutions to the generalized Abel integral equations …

We investigate the existence of solutions for a sum-type fractional integro-differential
problem via the Caputo differentiation. By using the shifted Legendre and Chebyshev …

The main aim of the current article is to describe an uni-dimensional moving boundary
problem with conduction and convection effect when thermal conductivity and specific heat …

In this article, a mathematical model describing the process of heat transfer in biological
tissues with blood perfusion having different values under different temperature range for …

A numerical method is developed for solving the Abel s integral equations is presented. The
method is based upon Hermite wavelet approximations. Hermite wavelet method is then …

The goal of this paper is to present a new scheme based on the stochastic arithmetic (SA) to
find the optimal convergence control parameter, the optimal iteration and the optimal …

In this article, the Legendre wavelet operational matrix of integration is used to solve
boundary ordinary differential equations with non-analytic solution. Although the standard …

A new operational matrix for integration of Bernoulli polynomials is introduced. By using this
new operational matrix of integration and the so-called collocation method, linear Volterra …