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

3. FIGURE 15.1.1 Planar region R with boundary C

4. FIGURE 15.1.2 Region R overlaid with rectangular grid

5. FIGURE 15.1.3 Square region R for Example 1

6. FIGURE 15.1.4 Region R in Example 1 with additional mesh points

7. TABLE

8. FIGURE 15.1.5 Rectangular region R

9. FIGURE 15.1.6 Region for Problem 6

10. FIGURE 15.1.7 Region for Problem 7

11. FIGURE 15.1.8 Region for Problem 8

12. FIGURE 15.2.1 Rectangular region in xt-plane

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

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

15. TABLE

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

17. TABLE

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

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

20. TABLE

21. TABLE

22. TABLE 15.R.1

23. TABLE 15.R.2