Explanation Given: The initial value problem is, x ′ ′ + ( 0.1 ) ( 1 − x 2 ) x ′ + x = 0 x ( 0 ) = x 0 x ′ ( 0 ) = 0 Step-size, h = 0.02 Approach: To compute an approximation for the solution to the given initial value problem over the interval [ 0 , t ] , use a programmed version of the vectorized classical fourth-order Runge-Kutta algorithm with step-size h . Calculation: To compute an approximation for the solution to the given initial value problem over the interval [ 0 , 20 ] , x ′ ′ + ( 0.1 ) ( 1 − x 2 ) x ′ + x = 0 x ′ ′ = − ( 0.1 ) ( 1 − x 2 ) x ′ − x x ( 0 ) = x 0 x ′ ( 0 ) = 0 Here x 0 takes values 1 and 2.1 . Use a programmed version of the vectorized classical fourth-order Runge-Kutta algorithm with step-size h and Initial values, x ( 0 ) = 1 x ′ ( 0 ) = 0 As shown in figure ( 1 ) , figure ( 2 ) , and table ( 1 ) . Figure ( 1 )

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Chapter 5.3, Problem 22E

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The solution x for the given initial value problem over the interval [0,20] exhibits damped oscillations for x0=1, and expanding oscillations for x0=2.1.

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Chapter 5.3, Problem 21E

Chapter 5.3, Problem 24E

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To illustrate: The solution x for the given initial value problem over the interval [ 0 , 20 ] exhibits damped oscillations for x 0 = 1 , and expanding oscillations for x 0 = 2.1 .

Solution Summary: The author illustrates the solution to the given initial value problem over the interval left[0,20right] using a programmed version of the vectorized classical fourth-order Runge-Kutta

Videos

To illustrate:

The solution x for the given initial value problem over the interval [0,20] exhibits damped oscillations for x0=1, and expanding oscillations for x0=2.1.

Want to see the full answer?

Chapter 5 Solutions

To illustrate: The solution x for the given initial value problem over the interval [ 0 , 20 ] exhibits damped oscillations for x 0 = 1 , and expanding oscillations for x 0 = 2.1 .

Solution Summary: The author illustrates the solution to the given initial value problem over the interval left[0,20right] using a programmed version of the vectorized classical fourth-order Runge-Kutta

Videos

To illustrate: The solution x for the given initial value problem over the interval [0,20] exhibits damped oscillations for x0=1, and expanding oscillations for x0=2.1.

Want to see the full answer?

Chapter 5 Solutions

To illustrate:

The solution x for the given initial value problem over the interval [0,20] exhibits damped oscillations for x0=1, and expanding oscillations for x0=2.1.