Elements of Electromagnetics -Sadiku

15.3 THE FINITE DIFFERENCE METHOD 669 Figure 15.5 For Practice Exercise 15.1. 15.3 THE FINITE DIFFERENCE METHOD The

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15.3

THE FINITE DIFFERENCE METHOD

669

Figure 15.5 For Practice Exercise 15.1.

15.3 THE FINITE DIFFERENCE METHOD The finite difference method1 (FDM) is a simple numerical technique used in solving problems like those solved analytically in Chapter 6. A problem is uniquely defined by three things:

1. A partial differential equation such as Laplace's or Poisson's equations 2. A solution region 3. Boundary and/or initial conditions

A finite difference solution to Poisson's or Laplace's equation, for example, proceeds in three steps: (1) dividing the solution region into a grid of nodes, (2) approximating the differential equation and boundary conditions by a set of linear algebraic equations (called difference equations) on grid points within the solution region, and (3) solving this set of algebraic equations.

'For an extensive treatment of the finite difference method, see G. D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, 2nd edition. Oxford: Clarendon, 1978.

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