Applications of Pseudospectral Methods

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During the past few years, pseudospectral or orthogonal collocation methods have been successfully used to solve a wide variety of applied problems, owing to its efficiency and high order of accuracy. The three most commonly used sets of collocation points are Gauss, Gauss-Radau, and Gauss-Lobatto points. On bounded domains, pseudospectral methods are usually based on Jacobi polynomials or even nonclassical orthogonal polynomials which provide a greater flexibility. Pseudospectral methods can be categorized into global (single-interval) and adaptive (multiple-interval) schemes. Whilst global pseudospectral methods provide exponential convergence for smooth solutions, adaptive pseudospectral methods increase the utility of pseudospectral methods for non-smooth solutions. The goal of this book is to explain some new applications of classical and nonclassical pseudospectral methods (both global and adaptive) for the numerical solution of classic and fractional variational problems, time-delay systems and their optimal control as well as for solving fractional differential equations.