Spectral Collocation Solutions to Problems on Unbounded Domains - Calin-Ioan Gheorghiu

Contents:

Interpolation on Unbounded Itervals
Iterpolation problem
Hermite and Sinc functions
Hermite functions
Hermite collocation
Sinc functions
Sinc collocation
Laguerre functions
1. 3. 1. The rate of convergence of polynominal Laguerre series

1. 3. 2. Laguerre collocation

1. 3. 3. Laguerre Gauss Radau collocation

1. 4. Mapping techniques

1. 4. 1. Preconditioned differentiation

1. 5. Miscellanies

1. 5. 1. The rate of convergence of eigeunfunction expansion

1. 5. 2. Polynominal transforms

1. 5. 3. Boundary condition implementation

1D Problems on Unbounded Domains
Some t. p. b. v. p. on the half line
Linear second order t. p. b. v. p
The Heun’s equation
Global solutions to a class of nonlinear second order  t. p. b. v. p.
Systems of t. p. b. v. p.
Another boundary layer type problem
T. p. b. v. p. on the real line
The order of approximation for SiC
SiC vs. HC for t. p. b. v. p. on the real line
Eigenvalue Problems
Singular eigenvalue problems on the half line
”Good” and ”bad” eigenvalues
Problems with parameter dependent boundary conditions
Schrödinger eigenvalue problems on the half line
A singular SturmLiouville problem with a complex potential
The Orr-Sommerfeld problem for boundary-layer flows
A fourth order singular eigenvalue problem
Singular eigenvalue problems on the reali line
The eigenfunctions orthogonality as a check of the accuracy
Continuous spectra and numerical eigenvalues
Solving algebraic generalized eigenvalue problems
Problems Attached to P. D. E.
Multidimensional problems reductive to t. p. b. v. p.
MoL for second order parabolic p. d. e.
The normality of D(2)H  and D(2)Si matrices
The region of absolute stability of TR-BDF2 finite difference scheme
Unsteady diffusion equation on the half line
Viscous Burgers’ equation on the real line
Fischer’s equation
The BBM type equations
HC and SiC solutions to BBm
Conservation of the energy intergral
An i. v. p. for Fokker-Planck equation
The KdV equation
Linear Schrödinger equation
The NLS equation
General-power Schrödinger equation
Waveguide solutions to the cubic NLS equation
Blow-up self similar solutions to the cubic NLS equation
Radially symmetric solutions to NLS
An envelope soliton problem attached to NLS
MATLAB scripts
Boundary value problems
Blasius boundary value problem
A singular nonlinear t. p. b. v. p.
Eigenvalue problems
 A fourth-order eigenvalue problem on half time
An second order eigenvalue problem on the real line
Initial value problems
Concluding  remarks and open problems