Finite difference methods have become a cornerstone in the simulation of seismic wave propagation, providing a robust numerical framework to approximate the differential equations that govern seismic ...

SIAM Journal on Numerical Analysis, Vol. 26, No. 6 (Dec., 1989), pp. 1474-1486 (13 pages) An explicit finite difference algorithm is developed to approximate the solution of a nonlinear and nonlocal ...

We consider the application of finite-difference methods to the numerical solution of boundary-value problems. In particular we are concerned to study the feasibility and convergence of the difference ...

This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...

My main research interests are in developing, analyzing, and implementing numerical methods, in particular for solving PDEs to high orders of accuracy. Such methods include pseudospectral and high ...