Book edition 9th

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

Pages 616 pages

ISBN 9780321977069

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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 for systems with $h = 0.175$ , approximate the solution to the initial value problem $x' = 2 x - y; x (0) = 0, y' = 3 x + 6 y; y (0) = - 2$ at $t = 1$ .
Compare this approximation to the actual solution.

The solution is $y (1) = - 423.48$ and $x (1) = 127.77$ .

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Step by Step Solution

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TABLE OF CONTENTS

Transform the equation

Write the equation as $x' = 2 x - y$ and $y' = 3 x + 6 y$

The transformation of the equation is:

$x'_{1} (t) = x_{2} (t) x_{1} (t) = y (t) x_{2} (t) = 2 x - x_{1} x'_{2} (t) = y' ((t) x'_{2} (t) = 3 x + 6 x_{1} (t)$

The initial conditions are:

$x (0) = 0 y (1) = - 2$

Apply Runge –Kutta method

For the solution, apply the Runge-Kutta method in MATLAB, and the solution is $y (1) = - 423.48$ and $x (1) = 127.77$ .

Compare this approximation to the actual solution x(t)=e5t-e3t,y(t)=e3t-3e5t

By putting the value of $t = 1$

$x (1) = e^{5} - e^{3} = 128.32 y (1) = e^{3} - 3 e^{5} = - 425.15$

Therefore, the approximation solution is $x (1) = 128.32$ and $y (1) = - 425.15$ .

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Fundamentals Of Differential Equations And Boundary Value Problems

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Short Answer

Step by Step Solution

Transform the equation

Apply Runge –Kutta method

Compare this approximation to the actual solution x(t)=e5t-e3t,y(t)=e3t-3e5t

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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

Compare this approximation to the actual solution x(t)=e5t-e3t,y(t)=e3t-3e5t

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