1550078481-Ordinary_Differential_Equations__Roberts_

Answers to Selected Exercises 543

1. c. En ::; .000004167 d. h ::; .059
   
   
   1. b. 3. 5.
      Taylor Series Improved Fourth-Order Exact
      Xn Order^3 Euler Runge-Kutta Solution
   
   
   
   

.0 1.000000 1.000000 1.000000 1.000000

.1 .905167 .905500 .905163 .905163

.2 .821277 .821928 .821270 .821269

.3 .749192 .750145 .749182 .749182

.4 .689692 .690931 .689681 .689680

.5 .643483 .644992 .643470 .643469

.6 .611203 .612968 .611189 .611188

.7 .593430 .595436 .593416 .593415

.8 .590687 .592920 .590672 .590671

.9 .603447 .605892 .603431 .603430

1.0 .632137 .634782 .632121 .632121

1

b = ~

2

7. a = - c = d = -
   4 ' 4' 3

Exercises 2 .4.2 Multistep Metho d s

1. b. .000417 c. .010626


2. a. Yn+l = [Yn(2 - h) + h(x~ + X~+i)J/(2 + h)
   
   
   1. a. 3. b.
      Adams- Adams-
      Bashforth Moulton Exact
      Xn m=O m=O solution
   
   
   
   

.o 1.000000

.1 .905238 .905163

.2 .820888 .821406 .821269

.3 .748513 .749367 .749182

.4 .688781 .6899 04 .689680

.5 .642389 .643722 .643469

.6 .609970 .611463 .6^11188

.7 .592094 .593705 .593415

.8 .589278 .590971 .590671

.9 .60199^1 .603736 .603430

1.0 .630656 .632427 .632121