Book edition 9th

Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider

Pages 616 pages

ISBN 9780321977069

Answers without the blur.

Just sign up for free and you're in.

Short Answer

In Problems 14–24, you will need a computer and a programmed version of the vectorized classical fourth-order Runge–Kutta algorithm. (At the instructor’s discretion, other algorithms may be used.)†
Using the vectorized Runge–Kutta algorithm, approximate the solution to the initial value problem
$\frac{du}{dx} = 3 u - 4 v; u (0) = 1' \frac{dv}{dx} = 2 u - 3 v; v (0) = 1$
at x = 1. Starting with h=1, continue halving the step size until two successive approximations of u(1)and v(1) differ by at most 0.001.

The solution is $u (1) = 0.36789$ and $v (1) = 0.36789$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Transform the equation

Write the equation as $u' = 3 u - 4 v$ and $v' = 2 u - 3 v$ .

The transformation of the equation is:

$u' (t) = x'_{2} (t) v' (t) = x_{3} (t) x_{2} (t) = v (t) x_{1} = u (t) x'_{2} (t) = 3 x_{1} - 4 x_{2} x'_{3} (t) = 2 x_{1} - 3 x_{2}$

The initial conditions are

$u (0) = 1 v (0) = 1$

Apply Runge –Kutta method

For the solution apply the Runge-Kutta method in MATLAB for h=0.25, and the solution is u(1)=0.36789 and v(1)=0.36789.

Find that u1 and v(1) differ by at most 0.001.

Subtracting the values of $u (1)$ and $v (1)$ then

$u (1) - v (1) = 0.36789 - 0.36678 = 0.001101$

Therefore, $u (1)$ and $v (1)$ differ by at most 0.001.

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

Step by Step Solution

Transform the equation

Apply Runge –Kutta method

Find that u1 and v(1) differ by at most 0.001.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

Step by Step Solution

Transform the equation

Apply Runge –Kutta method

Find that u1 and v(1) differ by at most 0.001.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths