Modified Fourier expansions present an alternative to more standard algorithms for the approximation of nonperiodic functions in bounded domains. This thesis addresses the theory of such expansions, their effective ...

This thesis presents methods for efficient numerical approximation of linear and non-linear systems of highly oscillatory ordinary differential equations. Phenomena of high oscillation is considered a major computational ...

The subject matter of this dissertation is the design, analysis and practical implementation of a new numerical method to approximate the eigenvalues and eigenfunctions of regular Sturm–Liouville problems, given in Liouville’s ...