The governing equations for this problem can be discretized with respect to t into P points with step [tau]=[theta]/(P-1) and x into N points with step h=1/(N-1) by rewriting them as the

finite-difference equations that are given by

Following Yee's notation and using centered difference approximation on both of the time and space first-order partial differentiations, six coupled scalar

finite-difference equations for six unique field components within a unit cell are obtained.

R., "High-accuracy

finite-difference equations for dielectric waveguide analysis I: Uniform regions and dielectric interfaces," Journal of Lightwave Technology, Vol.

In section 3, the

finite-difference equations are formulated.

The

finite-difference equations written for cells lying at the TF/SF interface contain both TF and SF quantities.

of British Columbia-Vancouver) explains how to use Lie groups with

finite-difference equations, meshes, and difference functionals, for practitioners, researchers, and graduate students in applied mathematics, physics, mechanics, and engineering.

The computations of U, V, T and C at time level (n +1) using the values at previous time level (n) are carried out as follows: The

finite-difference equations (15) and (18) at every internal nodal point on a particular i-level constitute a tridiagonal system of equations.

For dry coils, the implicit

finite-difference equations are linear and the method does not require iteration for state variables within each row.

Then it is divided into a number of control volumes along the airstream, and the one-dimensional differential equations are converted into

finite-difference equations within each control volume.

In the

finite-difference equations, the first subscript, i, denotes the region of the die, and the second subscript, j, represents the nodal position.

R., "High-accuracy

finite-difference equations for dielectric waveguide analysis II: Dielectric corners," Journal of Lightwave Technology, Vol.

A set of

finite-difference equations written about each mesh point in a column for the equation (7) as shown: