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 Scientific Computing
SIAM Journal on Scientific Computing
Optimal Error Estimates of the Legendre--Petrov--Galerkin Method for the Korteweg--de Vries Equation
SIAM Journal on Numerical Analysis
A Legendre--Petrov--Galerkin and Chebyshev Collocation Method for Third-Order Differential Equations
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Optimal Spectral-Galerkin Methods Using Generalized Jacobi Polynomials
Journal of Scientific Computing
Journal of Computational and Applied Mathematics
Optimal Gegenbauer quadrature over arbitrary integration nodes
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Hi-index | 0.01 |
Some efficient and accurate algorithms based on ultraspherical-dual-Petrov-Galerkin method are developed and implemented for solving (2n+1)th-order linear elliptic differential equations in one variable subject to homogeneous and nonhomogeneous boundary conditions using a spectral discretization. The key idea to the efficiency of our algorithms is to use trial functions satisfying the underlying boundary conditions of the differential equations and the test functions satisfying the dual boundary conditions. The method leads to linear systems with specially structured matrices that can be efficiently inverted. Numerical results are presented to demonstrate the efficiency of our proposed algorithms.