Numerical Solutions of Partial Differential Equations Chapter 15 Numerical Solutions of Partial Differential Equations

FIGURE 15.1.1 Planar region R with boundary C

FIGURE 15.1.2 Region R overlaid with rectangular grid

FIGURE 15.1.3 Square region R for Example 1

FIGURE 15.1.4 Region R in Example 1 with additional mesh points

TABLE 15.1.1

FIGURE 15.1.5 Rectangular region R

FIGURE 15.1.6 Region for Problem 6

FIGURE 15.1.7 Region for Problem 7

FIGURE 15.1.8 Region for Problem 8

FIGURE 15.2.1 Rectangular region in xt-plane

FIGURE 15.2.2 u at t = j + 1 is determined from three values of u at t = j

TABLE 15. 2. 1 Explicit Difference Equation Approximation with h = 0 TABLE 15.2.1 Explicit Difference Equation Approximation with h = 0.2, k = 0.01,  = 0.25

TABLE 15.2.2

TABLE 15.2.3 Crank-Nicholson Method with h = 0.25, k = 0.01,  5 0.25

TABLE 15.2.4

FIGURE 15.3.1 u at t = j + 1 is determined from three values of u at t = j and one value at t = j − 1.

TABLE 15. 3. 1 Explicit Difference Equation Approximation with h = 0 TABLE 15.3.1 Explicit Difference Equation Approximation with h = 0.2, k = 0.05,  = 0.5

TABLE 15.3.2

TABLE 15.3.3

TABLE 15.R.1

TABLE 15.R.2