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Chapter 1: Q5.3-16E (page 1)

In Problems 14鈥�24, you will need a computer and a programmed version of the vectorized classical fourth-order Runge鈥揔utta algorithm. (At the instructor鈥檚 discretion, other algorithms may be used.)鈥�

Using the vectorized Runge鈥揔utta algorithm for systems withh=0.175, approximate the solution to the initial value problemx'=2x-y;x(0)=0,y'=3x+6y;y(0)=-2 att=1.

Compare this approximation to the actual solution.

Short Answer

Expert verified

The solution isy1=-423.48and x1=127.77.

Step by step solution

01

Transform the equation

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

The transformation of the equation is:

x'1t=x2tx1t=ytx2t=2x-x1x'2t=y'(tx'2t=3x+6x1t

The initial conditions are:

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

02

Apply Runge –Kutta method

For the solution, apply the Runge-Kutta method in MATLAB, and the solution isy1=-423.48 and x1=127.77.

03

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

By putting the value oft=1

x1=e5-e3=128.32y1=e3-3e5=-425.15

Therefore, the approximation solution isx1=128.32 and y1=-425.15.

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Most popular questions from this chapter

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