# finite-difference equations

## finite-difference equations

[¦fī‚nīt ¦dif·rəns i‚kwā·zhənz]
(mathematics)
Equations arising from differential equations by substituting difference quotients for derivatives, and then using these equations to approximate a solution.
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References in periodicals archive ?
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:

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