Theoretical results of one class of multiderivative methods through order stars

Order stars are applied to Brown (K,L) methods. They are displayed pictorially for a selection of methods and are used to provide succinct proofs of existing results. Asymptotic results concerning their stability are also presented

A collocation method for solving singular integro-differential equations

This paper describes a collocation method for numerically solving Cauchy-type linear singular integro-differential equations. The numerical method is based on the transformation of the integro-differential equation into an integral equation, and then applying a collocation method to solve the latter. The collocation points are chosen as the Chebyshev nodes. Uniform convergence of the resulting method is then discussed. Numerical examples are presented and solved by the numerical techniques.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fapesp[2004/16064-9]CNPq[301787/2008-5]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq