We propose and analyze a spectral Jacobi-collocation approximation for the linear Volterra
integral equations (VIEs) of the second kind with weakly singular kernels. In this work, we …

In this paper, by combined homotopy analysis method and Laplace transform method, we
produce a new powerful method and named homotopy analysis transform method. By using …

Multistep collocation methods for Volterra integro-differential equations are derived and
analyzed. They increase the order of convergence of classical one-step collocation …

It is the purpose of this paper to provide an acceleration of waveform relaxation (WR)
methods for the numerical solution of large systems of ordinary differential equations. The …

In this paper, the numerical method for solving Abel's integral equations is presented. This
method is based on fractional calculus. Also, Chebyshev polynomials are utilized to apply …

In this paper, the convergence analysis of the Volterra integral equation of second kind with
weakly singular kernel and pantograph delays is provided. We use some function …

We introduce domain decomposition methods of Schwarz waveform relaxation (WR) type for
fractional diffusion-wave equations. We show that the Dirichlet transmission conditions …

Non-stationary discrete time waveform relaxation methods for Abel systems of Volterra
integral equations using fractional linear multistep formulae are introduced. Fully parallel …

This paper presents the application of a new powerful method named as q-homotopy
analysis transform method (q-HATM). The q-HATM is a combination of the q-homotopy …

The purpose of this paper is to employ graphics processing units for the numerical solution
of large systems of weakly singular Volterra Integral Equations (VIEs), by means of …