Question
In: Advanced Math
Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the recursion...
Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the recursion of (3) in Section 2.6
yn + 1 = yn + hf(xn, yn) (3)
by hand, first using
h = 0.1
and then using
h = 0.05.
y' = 2x − 3y + 1, y(1) = 8; y(1.2)
| y(1.2) | ≈ | (h = 0.1) |
| y(1.2) | ≈ | (h = 0.05) |
Solutions
Colby Messinger answered 2 years agoRelated Solutions
1) Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the...
1) Use Euler's method to obtain a four-decimal approximation of
the indicated value. Carry out the recursion of (3) in Section
2.6
yn + 1 = yn + hf(xn,
yn) (3)
by hand, first using h = 0.1 and then using h = 0.05.
y' = 2x − 3y + 1, y(1) = 4; y(1.2)
y(1.2)
≈
(h = 0.1)
y(1.2)
≈
(h = 0.05)
2)Use Euler's method to obtain a four-decimal approximation of
the indicated value. Carry out the recursion of...
Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value....
Use a numerical solver and Euler's method to obtain a
four-decimal approximation of the indicated value. First use
h = 0.1
and then use
h = 0.05
y' = y − y2, y(0) =
0.8; y(0.5)
y(0.5)
≈
? (h = 0.1)
y(0.5)
≈
? (h = 0.05)
Use the improved Euler's method to obtain a four-decimal approximation of the indicated value. First use...
Use the improved Euler's method to obtain a four-decimal
approximation of the indicated value. First use h = 0.1 and then
use h = 0.05. y' = y − y^2, y(0) = 0.8; y(0.5) y(0.5) ≈________ (h
= 0.1)
y(0.5) ≈ _________(h = 0.05)
Exercise (a) Use Euler's method with each of the following step sizes to estimate the value...
Exercise (a)
Use Euler's method with each of the following step sizes to
estimate the value of y(1.6), where y is the
solution of the initial-value problem y' = y,
y(0) = 6.
(i) h = 1.6
(ii) h = 0.8
(iii) h = 0.4
Exercise (b)
We know that the exact solution of the initial-value problem in
part (a) is y = 6ex. Draw, as
accurately as you can, the graph of y =
6ex, 0 ≤ x ≤ 1.6, together
with...
Use Euler's method with each of the following step sizes to estimate the value of y(0.8),...
Use Euler's method with each of the following step sizes to
estimate the value of y(0.8), where y is the
solution of the initial-value problem: y' = y,
y(0) = 5.
(i) h = 0.8
y(0.8) = 9
(ii) h = 0.4
y(0.8) = 9.8
(iii)
h = 0.2
y(0.8) = ?
The error in Euler's method is the difference between the exact
value and the approximate value. Find the errors made in part (a)
in using Euler's method to estimate...
Use Newton's method to approximate the indicated root of the equation correct to six decimal places....
Use Newton's method to approximate the indicated root of the
equation correct to six decimal places.
The root of x4 − 2x3 + 4x2 − 8
= 0 in the interval [1, 2]
x = ?
Decimal value data types such as float and double represent the decimal number as an approximation....
Decimal value data types such as float and double represent the
decimal number as an approximation. In other words, float or double
arithmetic do not give exact answer but near approximation to the
answer. As an example, run the following program and check its
result:
#include <iostream>
using namespace std;
int main()
{
float x= 0.1 * 7; if (x == 0.7)
cout<< "TRUE. \n"; else
cout<< "FALSE. \n"; return 0;
}
In some situations, we need our programs to...
Decimal value data types such as float and double represent the decimal number as an approximation....
Decimal value data types such as float and double represent the
decimal number as an approximation. In other words, float or double
arithmetic do not give exact answer but near approximation to the
answer. As an example, run the following program and check its
result:
#include <iostream>
using namespace std;
int main()
{
float x= 0.1 * 7;
if (x == 0.7)
cout<< "TRUE. \n";
else
cout<< "FALSE. \n";
return 0;
}
In some situations, we need our programs to...
Test the given claim. Use the P-value method or the traditional method as indicated. Identify the...
Test the given claim. Use the P-value method or the traditional
method as indicated. Identify the null hypothesis, alternative
hypothesis, test statistic, critical value(s) or P-value,
conclusion about the null hypothesis, and final conclusion that
addresses the original claim.
The mean resting pulse rate for men is 72 beats per minute. A
simple random sample of men who regularly work out at Mitch's Gym
is obtained and their resting pulse rates (in beats per minute) are
listed below. Use a...
Use the finite difference method and the indicated value of n to approximate the solution of...
Use the finite difference method and the indicated value of
n to approximate the solution of the given boundary-value
problem. (Round your answers to four decimal places.)
x2y'' +
3xy' + 5y =
0, y(1) =
6, y(2) =
0; n = 8
x
y
1.000
?
1.125
?
1.250
?
1.375
?
1.500
?
1.625
?
1.750
?
1.875
?
2.000
?
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