1. Solve the following problems using Euler's method with stepsizes of h = 0.2, 0.1, 0.05. Compute the error and relative error using the true answer Y(x). For selected values of x, observe the ratio by which the error decreases when h is halved. (a) Y'(x)= [cos(Y(x))]², Y(x) = tan¹(x) 0≤ x ≤ 10, Y(0) = 0; 1 (b) Y'(x)= 2[Y(x)]², 0≤ x ≤ 10, Y(0) = 0; 1+x² X Y(x) = 1+x²
1. Solve the following problems using Euler's method with stepsizes of h = 0.2, 0.1, 0.05. Compute the error and relative error using the true answer Y(x). For selected values of x, observe the ratio by which the error decreases when h is halved. (a) Y'(x)= [cos(Y(x))]², Y(x) = tan¹(x) 0≤ x ≤ 10, Y(0) = 0; 1 (b) Y'(x)= 2[Y(x)]², 0≤ x ≤ 10, Y(0) = 0; 1+x² X Y(x) = 1+x²
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![1. Solve the following problems using Euler's method with stepsizes of h = 0.2, 0.1,
0.05. Compute the error and relative error using the true answer Y(x). For selected
values of x, observe the ratio by which the error decreases when h is halved.
(a) Y'(x)= [cos(Y(x))]²,
Y(x) = tan¹(x)
0≤ x ≤ 10,
Y(0) = 0;
1
(b) Y'(x)=
2[Y(x)]²,
0≤ x ≤ 10,
Y(0) = 0;
1+x²
X
Y(x) =
1+x²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98010ec1-9ca3-4b08-b004-c204532892b9%2Fe5a4b856-73b2-4872-83a4-a13578a47868%2Foyk53n_processed.png&w=3840&q=75)
Transcribed Image Text:1. Solve the following problems using Euler's method with stepsizes of h = 0.2, 0.1,
0.05. Compute the error and relative error using the true answer Y(x). For selected
values of x, observe the ratio by which the error decreases when h is halved.
(a) Y'(x)= [cos(Y(x))]²,
Y(x) = tan¹(x)
0≤ x ≤ 10,
Y(0) = 0;
1
(b) Y'(x)=
2[Y(x)]²,
0≤ x ≤ 10,
Y(0) = 0;
1+x²
X
Y(x) =
1+x²
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