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- The method of fundamental solutions applied to boundary value problems on the surface of a spherePublication . Alves, Carlos J. S.; Antunes, Pedro R. S.In this work we propose using the method of fundamental solutions (MFS) to solve boundary value problems for the Helmholtz–Beltrami equation on a sphere. We prove density and convergence results that justify the proposed MFS approximation. Several numerical examples are considered to illustrate the good performance of the method.
- Analysis of a class of boundary value problems depending on left and right Caputo fractional derivativesPublication . Antunes, Pedro R. S.; Ferreira, Rui A. C.In this work we study boundary value problems associated to a nonlinear fractional ordinary differential equation involving left and right Caputo derivatives. We discuss the regularity of the solutions of such problems and, in particular, give precise necessary conditions so that the solutions are C1([0, 1]). Taking into account our analytical results, we address the numerical solution of those problems by the augmented-RBF method. Several examples illustrate the good performance of the numerical method.