Fourier series and boundary value problems

@inproceedings{Brown1938FourierSA,
  title={Fourier series and boundary value problems},
  author={James Ward Brown and Ruel Vance Churchill},
  year={1938}
}
Preface 1 Fourier Series Piecewise Continuous Functions Fourier Cosine Series Examples Fourier Sine Series Examples Fourier Series Examples Adaptations to Other Intervals 2 Convergence of Fourier Series One-Sided Derivatives A Property of Fourier Coefficients Two Lemmas A Fourier Theorem A Related Fourier Theorem Examples Convergence on Other Intervals A Lemma Absolute and Uniform Convergence of Fourier Series The Gibbs Phenomenon Differentiation of Fourier Series Integration of Fourier Series… Expand
Elementary Applied Partial Differential Equations With Fourier Series and Boundary Value Problems
1. Heat Equation. 2. Method of Separation of Variables. 3. Fourier Series. 4. Vibrating Strings and Membranes. 5. Sturm-Liouville Eigenvalue Problems. 6. An Elementary Discussion of Finite DifferenceExpand
Application of the Fourier cosine series to the approximation of solutions to initial non-Dirichlet boundary-value problems
T HE PAPER deals with an application of the Fourier cosine series to the determination of an approximate solution to some one-dimensional initial boundary-value problems. With the new approach oneExpand
Global series solutions of nonlinear differential equations with shocks using Walsh functions
  • P. Gnoffo
  • Mathematics, Computer Science
  • J. Comput. Phys.
  • 2014
TLDR
Fundamental operations (reciprocal, integral, derivative) on Walsh function series representations of functions with discontinuities are defined and examples are presented for solution of the time dependent Burger?s equation and for quasi-one-dimensional nozzle flow including a shock. Expand
An analytical solution for two-dimensional inverse heat conduction problems using Laplace transform
Abstract An analytical method has been developed for two-dimensional inverse heat conduction problems by using the Laplace transform technique. The inverse solutions are obtained under two simpleExpand
Analytical D’Alembert Series Solution for Multi-Layered One-Dimensional Elastic Wave Propagation with the Use of General Dirichlet Series
A general initial-boundary value problem of one-dimensional transient wave propagation in a multi-layered elastic medium due to arbitrary boundary or interface excitations (either prescribedExpand
A Fast Fourier-Boundary Element Method for axisymmetric potential and elasticity problems with arbitrary boundary conditions
Abstract This paper presents a new methodology, based on the Fast Fourier Transform (FFT), to solve axisymmetric potential and elasticity problems with arbitrary (non-axisymmetric) boundaryExpand
An exact solution of extended Graetz problem with axial heat conduction
Abstract The convective heat transfer properties of a hydrodynamically, fully developed viscous flow in a circular tube are analyzed without using any simplified assumption such as low ReynoldsExpand
Edge Detection Using Fourier Coefficients
TLDR
This paper discusses techniques for using a function's Fourier coefficients to determine the locations and sizes of the jump discontinuities of the function. Expand
Finite solid circular cylinders subjected to arbitrary surface load. Part I — Analytic solution
This paper presents a general framework for obtaining analytic solutions for finite elastic isotropic solid cylinders subjected to arbitrary surface load. The method of solution uses the displacementExpand
Higher order parallel splitting methods for parabolic partial differential equations
The thesis develops two families of numerical methods, based upon new rational approximations to the matrix exponential function, for solving secondorder parabolic partial differential equations.Expand
...
1
2
3
4
5
...