Transformations of matrices into banded form
Journal of Computational Physics
Spectral integration and two-point boundary value problems
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
An efficient spectral method for ordinary differential equations with rational function coefficients
Mathematics of Computation
Pseudospectral Solution of the Two-Dimensional Navier--Stokes Equations in a Disk
SIAM Journal on Scientific Computing
Spectral methods in MatLab
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Foundations of computational geometric mechanics
Foundations of computational geometric mechanics
Fourth-Order Time-Stepping for Stiff PDEs
SIAM Journal on Scientific Computing
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Journal of Computational and Applied Mathematics
Error estimates for deferred correction methods in time
Applied Numerical Mathematics
Is Gauss Quadrature Better than Clenshaw-Curtis?
SIAM Review
Computers & Mathematics with Applications
Numerical solutions of some nonlinear evolution equations by Chebyshev spectral collocation methods
International Journal of Computer Mathematics
Hi-index | 7.29 |
In solving semilinear initial boundary value problems with prescribed non-periodic boundary conditions using implicit-explicit and implicit time stepping schemes, both the function and derivatives of the function may need to be computed accurately at each time step. To determine the best Chebyshev collocation method to do this, the accuracy of the real space Chebyshev differentiation, spectral space preconditioned Chebyshev tau, real space Chebyshev integration and spectral space Chebyshev integration methods are compared in the L^2 and W^2^,^2 norms when solving linear fourth order boundary value problems; and in the L^~([0,T];L^2) and L^~([0,T];W^2^,^2) norms when solving initial boundary value problems. We find that the best Chebyshev method to use for high resolution computations of solutions to initial boundary value problems is the spectral space Chebyshev integration method which uses sparse matrix operations and has a computational cost comparable to Fourier spectral discretization.