arXiv subjects

Maria João Rodrigues

Publications and source records attributed to Maria João Rodrigues.

2 recordsLinked to original sources

arXiv2017

Explicit formulae for derivatives and primitives of orthogonal polynomials

In this work we deduce explicit formulae for the elements of the matrices that represent the action of integro-differential operators over the coefficients of generalized Fourier series. Our formulae are obtained by performing operations on the bases of orthogonal polynomials and result directly from the three-term recurrence relation satisfied by the polynomials. Moreover we give exact formulae for the coefficients for some families of orthogonal polynomials. Some tests are given to demonstrate the robustness of the formulas presented.

math.NA↗

arXiv2017

Filtering the Tau method with Frobenius-Padé Approximants

In this work, we use rational approximation to improve the accuracy of spectral solutions of differential equations. When working in the vicinity of solutions with singularities, spectral methods may fail their propagated spectral rate of convergence and even they may fail their convergence at all. We describe a Padé approximation based method to improve the approximation in the Tau method solution of ordinary differential equations. This process is suitable to build rational approximations to solutions of differential problems when their exact solutions have singularities close to their domain.

math.NA↗