Existence and nonexistence of solitary wave solutions to higher-order model evolution equations
SIAM Journal on Mathematical Analysis
The pseudospectral method for third-order differential equations
SIAM Journal on Numerical Analysis
Properties of collocation third-derivative operators
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
Journal of Approximation Theory
Optimal Spectral-Galerkin Methods Using Generalized Jacobi Polynomials
Journal of Scientific Computing
A Pseudospectral Fictitious Point Method for High Order Initial-Boundary Value Problems
SIAM Journal on Scientific Computing
Generalized Jacobi Rational Spectral Method and Its Applications
Journal of Scientific Computing
Computers & Mathematics with Applications
Sparse Spectral Approximations of High-Dimensional Problems Based on Hyperbolic Cross
SIAM Journal on Numerical Analysis
Generalized Jacobi rational spectral method on the half line
Advances in Computational Mathematics
Spectral Method for Navier---Stokes Equations with Slip Boundary Conditions
Journal of Scientific Computing
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We introduce a family of generalized Jacobi polynomials/functions with indexes @a,@b@?R which are mutually orthogonal with respect to the corresponding Jacobi weights and which inherit selected important properties of the classical Jacobi polynomials. We establish their basic approximation properties in suitably weighted Sobolev spaces. As an example of their applications, we show that the generalized Jacobi polynomials/functions, with indexes corresponding to the number of homogeneous boundary conditions in a given partial differential equation, are the natural basis functions for the spectral approximation of this partial differential equation. Moreover, the use of generalized Jacobi polynomials/functions leads to much simplified analysis, more precise error estimates and well conditioned algorithms.