Simon Fraser University

Finite Difference Approximations of Derivatives

First-order derivatives: n additional function calls are needed. Second-order derivatives based on gradient calls, when the "grd" module is specified (Dennis and Schnabel 1983): n additional gradient ...
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A Survey of Some Applications of Probability and Stochastic Control Theory to Finite Difference Methods for Degenerate Elliptic and Parabolic Equations

Finite difference methods for degenerate linear and (certain) nonlinear elliptic and parabolic equations are analyzed from a probabilistic point of view, and probabilistic methods are used to show ...
Risk

Numerical simulation and applications of the convection–diffusion–reaction equation with the radial basis function in a finite-difference mode

This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...
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Derivative Superconvergent Points in Finite Element Solutions of Harmonic Functions: A Theoretical Justification

Mathematics of Computation, Vol. 71, No. 240 (Oct., 2002), pp. 1421-1430 (10 pages) Finite element derivative superconvergent points for harmonic functions under local rectangular mesh are ...