Student Solutions Manual For Zill's A First Course In Differential Equations With Modeling Applications, 11th
11th Edition
ISBN: 9781305965737
Author: Dennis G. Zill
Publisher: Brooks Cole
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Textbook Question
Chapter 9.2, Problem 18E
Consider the initial-value problem y′ = 2x – 3y + 1, y(1) = 5. The analytic solution is
- (a) Find a formula involving c and h for the local truncation error in the nth step if the RK4 method is used.
- (b) Find a bound for the local truncation error in each step if h = 0.1 is used to approximate y(1.5).
- (c) Approximate y(1.5) using the RK4 method with h = 0.1 and h = 0.05. See Problem 3. You will need to carry more than six decimal places to see the effect of reducing the step size.
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Chapter 9 Solutions
Student Solutions Manual For Zill's A First Course In Differential Equations With Modeling Applications, 11th
Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - In Problems 110 use the improved Eulers method to...Ch. 9.1 - Prob. 4ECh. 9.1 - In Problems 110 use the improved Eulers method to...Ch. 9.1 - Prob. 6ECh. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - In Problems 110 use the improved Eulers method to...Ch. 9.1 - In Problems 110 use the improved Eulers method to...Ch. 9.1 - In Problems 110 use the improved Eulers method to...
Ch. 9.1 - Consider the initial-value problem y′ = (x + y –...Ch. 9.1 - Consider the initial-value problem y = 2y, y(0) =...Ch. 9.1 - Repeat Problem 13 using the improved Eulers...Ch. 9.1 - Repeat Problem 13 using the initial-value problem...Ch. 9.1 - Repeat Problem 15 using the improved Euler’s...Ch. 9.1 - Consider the initial-value problem y = 2x 3y + 1,...Ch. 9.1 - Repeat Problem 17 using the improved Euler’s...Ch. 9.1 - Repeat Problem 17 for the initial-value problem y′...Ch. 9.1 - Repeat Problem 19 using the improved Euler’s...Ch. 9.1 - Answer the question Why not? that follows the...Ch. 9.2 - Use the RK4 method with h = 0.1 to approximate...Ch. 9.2 - Assume that (4). Use the resulting second-order...Ch. 9.2 - In Problems 3–12 use the RK4 method with h = 0.1...Ch. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - In Problems 3–12 use the RK4 method with h = 0.1...Ch. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - If air resistance is proportional to the square of...Ch. 9.2 - Consider the initial-value problem y = 2y, y(0) =...Ch. 9.2 - Repeat Problem 16 using the initial-value problem...Ch. 9.2 - Consider the initial-value problem y′ = 2x – 3y +...Ch. 9.2 - Prob. 19ECh. 9.2 - Prob. 20ECh. 9.3 - Prob. 1ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - In Problems 58 use the Adams-Bashforth-Moulton...Ch. 9.4 - Use Eulers method to approximate y(0.2), where...Ch. 9.4 - Use Euler’s method to approximate y(1.2), where...Ch. 9.4 - Prob. 3ECh. 9.4 - In Problems 3 and 4 repeat the indicated problem...Ch. 9.4 - Prob. 5ECh. 9.5 - In Problems 110 use the finite difference method...Ch. 9.5 - Prob. 2ECh. 9.5 - Prob. 3ECh. 9.5 - Prob. 4ECh. 9.5 - Prob. 5ECh. 9.5 - Prob. 6ECh. 9.5 - Prob. 7ECh. 9.5 - In Problems 1 – 10 use the finite difference...Ch. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - The electrostatic potential u between two...Ch. 9.5 - Prob. 13ECh. 9 - In Problems 14 construct a table comparing the...Ch. 9 - In Problems 14 construct a table comparing the...Ch. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RE
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