The numerical calculation of traveling wave solutions of nonlinar parabolic equations
SIAM Journal on Scientific and Statistical Computing
Mathematics of Computation
Pseudo-spectral solution of nonlinear Schro¨dinger equations
Journal of Computational Physics
Fourth-order symplectic integration
Physica D
Computer Methods in Applied Mechanics and Engineering
An analysis of the fractional step method
Journal of Computational Physics
A novel method for simulating the complex Ginzburg-Landau equation
Quarterly of Applied Mathematics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
Nth-order operator splitting schemes and nonreversible systems
SIAM Journal on Numerical Analysis
Difference schemes for solving the generalized nonlinear Schrödinger equation
Journal of Computational Physics
Operator splitting methods for generalized Korteweg-de Vries equations
Journal of Computational Physics
A fast spectral algorithm for nonlinear wave equations with linear dispersion
Journal of Computational Physics
Spectral methods in MatLab
An analysis of operator splitting techniques in the stiff case
Journal of Computational Physics
Spectral methods for hyperbolic problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
Journal of Computational Physics
Journal of Computational Physics
High resolution conjugate filters for the simulation of flows
Journal of Computational Physics
SIAM Journal on Scientific Computing
A split step approach for the 3-D Maxwell's equations
Journal of Computational and Applied Mathematics
Numerical methods for the generalized Zakharov system
Journal of Computational Physics
A note on the numerical solution of high-order differential equations
Journal of Computational and Applied Mathematics
Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow
SIAM Journal on Scientific Computing
DSC time-domain solution of Maxwell's equations
Journal of Computational Physics
Numerical simulation of a generalized Zakharov system
Journal of Computational Physics
A Fourth-Order Time-Splitting Laguerre--Hermite Pseudospectral Method for Bose--Einstein Condensates
SIAM Journal on Scientific Computing
On a nonlinear diffusion equation describing population growth
IBM Journal of Research and Development
A windowed Fourier pseudospectral method for hyperbolic conservation laws
Journal of Computational Physics
A numerical study of the long wave-short wave interaction equations
Mathematics and Computers in Simulation
Journal of Computational Physics
Adaptive artificial boundary condition for the two-level Schrödinger equation with conical crossings
Journal of Computational Physics
Iterative Filtering Decomposition Based on Local Spectral Evolution Kernel
Journal of Scientific Computing
Operator splitting ADI schemes for pseudo-time coupled nonlinear solvation simulations
Journal of Computational Physics
Hi-index | 31.47 |
A family of local spectral evolution kernels (LSEKs) are derived for analytically integrating a class of partial differential equations (PDEs)@?@?tu=A(t)@?^2@?x^2+B(t)@?@?x+C(t)u.The LSEK can solve the above PDEs with x-independent coefficients in a single step. They are utilized in operator splitting schemes to arrive at a local spectral time-splitting (LSTS) method for solving more general linear and/or nonlinear PDEs. Like previous local spectral methods, this new method is of controllable accuracy in both spatial and temporal discretizations, and it can be of spectral accuracy in space and arbitrarily high-order accuracy in time. Its complexity scales as O(N) at a fixed level of accuracy. It is explicit, time transverse invariant, unconditionally stable for many problems whose two split parts are both analytically integrable. It adopts uniform grid meshes. The proposed method is extensively validated in terms of accuracy, stability, efficiency, robustness and reliability by the Fokker-Planck equation, the Black-Scholes equation, the heat equation, the plane wave propagation, the Zakharov system, and a linear harmonic oscillator. Numerical applications are considered to Fisher's equation, the generalized nonlinear Schrodinger equation, the Bose-Einstein condensates, and the Schrodinger equation in the semi-classical regime. Numerical results compare well with those in the literature.