Noise Analysis for Optical Fiber Communication Systems
Proceedings of the 2003 IEEE/ACM international conference on Computer-aided design
Journal of Computational Physics
Journal of Computational Physics
Generalized integrating factor methods for stiff PDEs
Journal of Computational Physics
Rooted tree analysis of Runge-Kutta methods with exact treatment of linear terms
Journal of Computational and Applied Mathematics
Efficient semi-implicit schemes for stiff systems
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
EXPINT---A MATLAB package for exponential integrators
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational Physics
Fourierization of the Legendre--Galerkin method and a new space--time spectral method
Applied Numerical Mathematics
An error analysis of the modified scaling and squaring method
Computers & Mathematics with Applications
A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales
Journal of Computational Physics
Velocity-induced numerical solutions of reaction-diffusion systems on continuously growing domains
Journal of Computational Physics
A rational Krylov method for solving time-periodic differential equations
Applied Numerical Mathematics
Compact integration factor methods in high spatial dimensions
Journal of Computational Physics
Lie group integrators with non-autonomous frozen vector fields
International Journal of Computational Science and Engineering
Exponential operator splitting time integration for spectral methods
Journal of Computational and Applied Mathematics
A time-adaptive finite volume method for the Cahn-Hilliard and Kuramoto-Sivashinsky equations
Journal of Computational Physics
Smoothing schemes for reaction-diffusion systems with nonsmooth data
Journal of Computational and Applied Mathematics
Approximation of matrix operators applied to multiple vectors
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
Comparison of methods for evaluating functions of a matrix exponential
Applied Numerical Mathematics
The scaling and modified squaring method for matrix functions related to the exponential
Applied Numerical Mathematics
Algorithm 894: On a block Schur--Parlett algorithm for ϕ-functions based on the sep-inverse estimate
ACM Transactions on Mathematical Software (TOMS)
A numerical simulation for the blow-up of semi-linear diffusion equations
International Journal of Computer Mathematics
Journal of Computational and Applied Mathematics
Rooted tree analysis of Runge-Kutta methods with exact treatment of linear terms
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
An exponential integrator for advection-dominated reactive transport in heterogeneous porous media
Journal of Computational Physics
L2-stability analysis of novel ETD scheme for Kuramoto-Sivashinsky equations
Journal of Computational and Applied Mathematics
Compact integration factor methods for complex domains and adaptive mesh refinement
Journal of Computational Physics
On a prey-predator reaction-diffusion system with Holling type III functional response
Journal of Computational and Applied Mathematics
Simulation of coherent structures in nonlinear Schrödinger-type equations
Journal of Computational Physics
Harmonic analysis for star graphs and the spherical coordinate trapezoidal rule
Journal of Computational and Applied Mathematics
Linearly implicit methods for nonlinear PDEs with linear dispersion and dissipation
Journal of Computational Physics
Journal of Computational Physics
A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK)
Journal of Computational Physics
A robust and efficient method for steady state patterns in reaction-diffusion systems
Journal of Computational Physics
Journal of Computational Physics
Fourth Order Time-Stepping for Kadomtsev-Petviashvili and Davey-Stewartson Equations
SIAM Journal on Scientific Computing
Time-stepping methods for the simulation of the self-assembly of nano-crystals in Matlab on a GPU
Journal of Computational Physics
Explicit exponential Runge-Kutta methods of high order for parabolic problems
Journal of Computational and Applied Mathematics
Exponential Rosenbrock methods of order five - construction, analysis and numerical comparisons
Journal of Computational and Applied Mathematics
Array-representation integration factor method for high-dimensional systems
Journal of Computational Physics
Reprint of "Explicit exponential Runge-Kutta methods of high order for parabolic problems"
Journal of Computational and Applied Mathematics
The Explicit-Implicit-Null method: Removing the numerical instability of PDEs
Journal of Computational Physics
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A modification of the exponential time-differencing fourth-order Runge--Kutta method for solving stiff nonlinear PDEs is presented that solves the problem of numerical instability in the scheme as proposed by Cox and Matthews and generalizes the method to nondiagonal operators. A comparison is made of the performance of this modified exponential time-differencing (ETD) scheme against the competing methods of implicit-explicit differencing, integrating factors, time-splitting, and Fornberg and Driscoll's "sliders" for the KdV, Kuramoto--Sivashinsky, Burgers, and Allen--Cahn equations in one space dimension. Implementation of the method is illustrated by short MATLAB programs for two of the equations. It is found that for these applications with fixed time steps, the modified ETD scheme is the best.