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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)
— 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)
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)