Chapter 9 Numerical Solutions of Ordinary Differential Equations

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Chapter 9 Numerical Solutions of Ordinary Differential Equations Dennis G. Zill, Differential Equations with

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

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,

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,

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

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.

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.

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.

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,

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

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,

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

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

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.

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

FIGURE 9. 4. 3 Network in Problem 6 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 15