Book Review: Fourier Series and Boundary Value Problems

Multivariate modified Fourier series and application to boundary value problems

In this paper we analyse the approximation-theoretic properties of modified Fourier series in Cartesian product domains with coefficients from full and hyperbolic cross index sets. We show that the number of expansion coefficients may be reduced significantly whilst retaining comparable error estimates. In doing so we extend the univariate results of Iserles, Nørsett and S. Olver. We then demon...

Univariate modified Fourier methods for second order boundary value problems

We develop and analyse a new spectral-Galerkin method for the numerical solution of linear, second order differential equations with homogeneous Neumann boundary conditions. The basis functions for this method are the eigenfunctions of the Laplace operator subject to these boundary conditions. Due to this property this method has a number of beneficial features, including an O(N) condition numb...

L2-transforms for boundary value problems

In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

Boundary Singularities of Faber and Fourier Series

Given an analytic Jordan curve with interior G and exterior and given a sequence of complex numbers fang n satisfying lim sup n janj n we consider here three series of the form f z X n anPn z where the polynomials Pn z are chosen to be i the Faber polynomials associated with G ii the polynomials orthogonal over the area of G and iii the polynomials orthogonal over the contour Here we study the ...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation