Adaptive High-Order Finite-Difference Method for Nonlinear Wave Problems
Journal of Scientific Computing
Journal of Scientific Computing
Method of lines study of nonlinear dispersive waves
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the 2nd international conference on advanced computational methods in engineering (ACOMEN2002) Liege University, Belgium, 27-31 May 2002
High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces
Journal of Computational Physics
Journal of Computational Physics
A MATLAB implementation of upwind finite differences and adaptive grids in the method of lines
Journal of Computational and Applied Mathematics - Special issue on the method of lines: Dedicated to Keith Miller
Method of lines solutions of the extended Boussinesq equations
Journal of Computational and Applied Mathematics - Special issue on the method of lines: Dedicated to Keith Miller
Adaptive method of lines solutions for the extended fifth-order Korteweg-de Vries equation
Journal of Computational and Applied Mathematics - Special issue on the method of lines: Dedicated to Keith Miller
Scattered node compact finite difference-type formulas generated from radial basis functions
Journal of Computational Physics
Journal of Computational Physics
Optimized high-order finite difference wave equations modeling on reconfigurable computing platform
Microprocessors & Microsystems
Journal of Computational Physics
Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
Journal of Computational Physics
A survey on various computational techniques for nonlinear elliptic boundary value problems
Advances in Engineering Software
Numerical pricing of options using high-order compact finite difference schemes
Journal of Computational and Applied Mathematics
A new time-space domain high-order finite-difference method for the acoustic wave equation
Journal of Computational Physics
A MATLAB implementation of upwind finite differences and adaptive grids in the method of lines
Journal of Computational and Applied Mathematics - Special issue on the method of lines: Dedicated to Keith Miller
Method of lines solutions of the extended Boussinesq equations
Journal of Computational and Applied Mathematics - Special issue on the method of lines: Dedicated to Keith Miller
Adaptive method of lines solutions for the extended fifth-order Korteweg-de Vries equation
Journal of Computational and Applied Mathematics - Special issue on the method of lines: Dedicated to Keith Miller
Simulating 2D Waves Propagation in Elastic Solid Media Using Wavelet Based Adaptive Method
Journal of Scientific Computing
An interpolation matched interface and boundary method for elliptic interface problems
Journal of Computational and Applied Mathematics
RBF-FD formulas and convergence properties
Journal of Computational Physics
Stabilization of RBF-generated finite difference methods for convective PDEs
Journal of Computational Physics
Linear Rational Finite Differences from Derivatives of Barycentric Rational Interpolants
SIAM Journal on Numerical Analysis
Stable calculation of Gaussian-based RBF-FD stencils
Computers & Mathematics with Applications
Optimized explicit finite-difference schemes for spatial derivatives using maximum norm
Journal of Computational Physics
A level set two-way wave equation approach for Eulerian interface tracking
Journal of Computational Physics
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The classical techniques for determining weights in finite difference formulas were either computationally slow or very limited in their scope (e.g., specialized recursions for centered and staggered approximations, for Adams--Bashforth-, Adams--Moulton-, and BDF-formulas for ODEs, etc.). Two recent algorithms overcome these problems. For equispaced grids, such weights can be found very conveniently with a two-line algorithm when using a symbolic language such as Mathematica (reducing to one line in the case of explicit approximations). For arbitrarily spaced grids, we describe a computationally very inexpensive numerical algorithm.