2.4 Finite Differences
www.iue.tuwien.ac.at › phd › heinzl2.4.2 Analysis of the Finite Difference Method One method of directly transfering the discretization concepts (Section 2.1) is the finite difference time domain method.It is analyzed here related to time-dependent Maxwell equations, as was first introduced by Yee [].
INTRODUCTION TO DISCRETIZATION
dslavsk.sites.luc.edu › courses › phys301consider the differential equation in eq. (1). This equation relates the second derivative of a function to the negative of the original function (times a constant). What functions do we know that when differentiated twice, return the negative of the original function? And the answer, as you learned in intro calc, are the sin and cos functions.
Discretization - Wikipedia
https://en.wikipedia.org/wiki/DiscretizationDiscretization is also concerned with the transformation of continuous differential equations into discrete difference equations, suitable for numerical computing. The following continuous-time state space modelwhere v and w are continuous zero-mean white noise sources with power spectral densitiescan be discretized, assuming zero-order holdfor the input u and continuous integration for the no…
Discrete Laplace operator - Wikipedia
https://en.wikipedia.org/wiki/Discrete_Laplace_operatorIn mathematics, the discrete Laplace operator is an analog of the continuous Laplace operator, defined so that it has meaning on a graph or a discrete grid.For the case of a finite-dimensional graph (having a finite number of edges and vertices), the discrete Laplace operator is more commonly called the Laplacian matrix.. The discrete Laplace operator occurs in physics …
Discretization of the Derivative Operator
gking.harvard.edu › files › gkingsecond derivative at x =1, we will make the choice n={−1,1,2,3}. Therefore, if we denote by f the vector whose elements are the values of the function f on an integer grid, its derivative of order j is the vector Djf, where Dj is a square matrix whose rows contain the weights that can be computed according to equation D.2. The matrix Dj is a ...
Finite difference - Wikipedia
https://en.wikipedia.org/wiki/Finite_differenceIn an analogous way, one can obtain finite difference approximations to higher order derivatives and differential operators. For example, by using the above central difference formula for f ′(x + h / 2) and f ′(x − h / 2) and applying a central difference formula for the derivative of f ′ at x, we obtain the central difference approximation of the second derivative of f: