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This work is concerned with the numerical solution of a nonlinear weakly singular Volterra integral equation. 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.… (More)
This paper is devoted to the numerical approximation of the diffusion equation with distributed order in time. A numerical method is proposed in the case where the order of the time derivative is distributed over the interval [0, 1], and results concerning the stability and convergence of that scheme are provided. Two numerical examples are presented… (More)
— In this paper we present a shooting algorithm to solve fractional terminal (or boundary) value problems. We provide a convergence analysis of the numerical method, derived based upon properties of the equation being solved and without the need to impose smoothness conditions on the solution. The work is a sequel to our recent investigation where we… (More)
In this work, we develop a meshfree method based on fundamental solutions basis functions for a transmission problem in linear elasticity. The problem here addressed, consists in computing the displacement field of an elastic object, which has piecewise constant Lamé coefficients , from a given displacement field on the boundary. The Lamé coefficients are… (More)
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.
A nonpolynomial collocation method for fractional terminal value problems. Abstract In this paper we propose a non-polynomial collocation method for solving a class of terminal (or boundary) value problems for differential equations of fractional order α, 0 < α < 1. The approach used is based on the equivalence between a problem of this type and a Fredholm… (More)