Polynomial Approximation of Differential Equations

This introduction to spectral methods for differential equations and time-dependent boundary-value problems gives the theoretical analysis of problems of convergence as well as numerical implementations.

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This book is a basic and comprehensive introduction to the use of spectral methods for the approximation of the solution to ordinary differential equations and time-dependent boundary-value problems. The algorithms are presented and studied both from the point of view of the theoretical analysis of convergence and the numerical implementation.