Chapter 9 Numerical Solutions of Ordinary Differential Equations
- Slides: 15
Chapter 9 Numerical Solutions of Ordinary Differential Equations Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018
Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 2
TABLE 9. 1. 1 Euler’s Method with h = 0. 1 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 3
TABLE 9. 1. 2 Euler’s Method with h = 0. 05 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 4
FIGURE 9. 1. 1 Slope of red dashed line is the average of m 0 and m 1 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 5
TABLE 9. 1. 3 Improved Euler’s Method with h = 0. 1 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 6
TABLE 9. 1. 4 Improved Euler’s Method with h = 0. 05 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 7
TABLE 9. 2. 1 RK 4 Method with h = 0. 1 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 8
TABLE 9. 2. 2 y´ = 2 xy, y(1) = 1 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 9
TABLE 9. 2. 3 RK 4 Method Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 10
FIGURE 9. 4. 1 Numerical solution curves generated by different methods Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 11
TABLE 9. 4. 1 h = 0. 2 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 12
TABLE 9. 4. 2 h = 0. 1 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 13
FIGURE 9. 4. 2 Numerical solution curves for IVP in Example 3 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 14
FIGURE 9. 4. 3 Network in Problem 6 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 15
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