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Friday, November 27, 2015

Scientific Computing - Quiz 4 - Problem 1, 2

Problem:

Consider the differential equation
y+yy+y2=cos(t)

which is the correct conversion of this equation into first-order form

Consider also the boundary conditions

y(0)=5,y(0)=3,y(1)y(1)+y(1)=0

What is the correct implementation of these boundary conditions in the first-order system.

Solution:

Let y1=y, y2=y, y3=y, we have

y1=y2
y2=y3
y3=y=cos(t)yyy2=cos(t)y1y2y21

y(0)=5y3(0)=5
y(0)=3y1(0)=3
y(1)y(1)+y(1)=0y1(1)y2(1)+y1(1)=0

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