This paper treats definite integrations numerically using Gegenbauer quadratures. The
novel numerical scheme introduces the idea of exploiting the strengths of the Chebyshev …

In this paper, we give an integration rectangular preconditioner for ultraspherical
pseudospectral operators. We present an explicit solution of matrix equations with the …

The main purpose of this work is to provide fractional pseudospectral integration matrices
(FPIMs) and apply them to solve fractional differential, integral, and integro-differential …

This paper reports a novel direct Gegenbauer (ultraspherical) transcription method (GTM) for
solving continuous-time optimal control (OC) problems (CTOCPs) with linear/nonlinear …

Analytic solutions of simple optimal control problems may be found using classical tools
such as the calculus of variations, dynamic programming or the minimum principle …

As the Tau method, like many other numerical methods, has the limitation of using a fixed
step size with some high degree (order) of approximation for solving initial value problems …

Spectral/pseudospectral integration preconditioning matrices are useful tools for solving
differential equations involving pure differential operators dm/dx m. In this study we construct …

Single domain spectral/pseudospectral integration preconditioning matrices have been
shown to be effective operators for solving differential equations. In this study we extend the …

A matrix representation of integration for arbitrary grids is introduced. Suitable results are
then obtained to be used along with differentiation matrix preconditioner to implement …

In this study we propose a construction framework utilizing stepwise integrations and the
Sherman-Morrison-Woodbury formula to seek pseudospectral integration preconditioning …