Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
The Taylor method of order 2 can be used to approximate the solution to the initial value problem y' = y. y(0)=1 at x = 1. Show that the approximation y obtained by using the Taylor method of order 2, with step size is given by the formula y₁=1+ The solution to the initial value problem is y=e*, so yn is an approximation of the constante. Let y'=f(x,y) and y'=f₂(x,y). If xn+1 = x +h, then which recursive formula, for Yn+1. represents the Taylor method of order 2? O A. Yn+1=Yn + f(xn-Yn) + 12 (xn-Yn) • Yn+1 = Yn +hf (x + 2₁ Yn + ²(xn³Yn)] OC. Yn+1+Yn+hf(xn+h. Yn+hf(xn-Yn)) OB. Yn+h h² OD. Yn+1=Yn+hf (XnYn) + 21¹2(Xn-Yn) In this case, what is the value of h? h=0 If y'=y, what can be said about each successive derivative of y? OA. Each successive derivative of y is equal to some constant C. OB. Each successive derivative of y is equal to 0. OC. Each successive derivative of y is equal to y plus some constant C OD. Each successive derivative of y is equal to y. Using the information in the previous step, find f₂(x,y). f₂(x,y) = Substitute the values of h, f(xnYn), and f₂ (XnYn) into the formula for Yn+1 Yn+1=0 for n = 1, 2

The Taylor method of order 2 can be used to approximate the solution to the initial value problem y' = y. y(0)=1 at x = 1. Show that the approximation y obtained by using the Taylor method of order 2, with step size is given by the formula y₁=1+ The solution to the initial value problem is y=e*, so yn is an approximation of the constante. Let y'=f(x,y) and y'=f₂(x,y). If xn+1 = x +h, then which recursive formula, for Yn+1. represents the Taylor method of order 2? O A. Yn+1=Yn + f(xn-Yn) + 12 (xn-Yn) • Yn+1 = Yn +hf (x + 2₁ Yn + ²(xn³Yn)] OC. Yn+1+Yn+hf(xn+h. Yn+hf(xn-Yn)) OB. Yn+h h² OD. Yn+1=Yn+hf (XnYn) + 21¹2(Xn-Yn) In this case, what is the value of h? h=0 If y'=y, what can be said about each successive derivative of y? OA. Each successive derivative of y is equal to some constant C. OB. Each successive derivative of y is equal to 0. OC. Each successive derivative of y is equal to y plus some constant C OD. Each successive derivative of y is equal to y. Using the information in the previous step, find f₂(x,y). f₂(x,y) = Substitute the values of h, f(xnYn), and f₂ (XnYn) into the formula for Yn+1 Yn+1=0 for n = 1, 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
1 is given by the formula y = The Taylor method of order 2 can be used to approximate the solution to the initial value problem y' = y, y(0) = 1 at x = 1. Show that the approximation y obtained by using the Taylor method of order 2, with step size n The solution to the initial value problem is y=e*, so yn is an approximation of the constante. Let y'=f(x,y) and y'' = f₂(x,y). If Xn+1 = X₁ +h, then which recursive formula, for Yn+1, represents the Taylor method of order 2? h O A. Yn+1=Yn + f(xn Yn) + ¹₂ (xn-Yn) h h • + h²{x₁ + 1 = ₁ yn + · +hf/xn- in + 1/{f(xnxn)) OC. Yn+1+Yn +hf(xn+h, Yn+hf(xn Yn)) O B. Yn+1=Yn+h h² OD. Yn+1=Yn +hf(xn-Yn) + 21¹2(XnYn) In this case, what is the value of h? h= If y' = y, what can be said about each successive derivative of y? O A. Each successive derivative of y is equal to some constant C. O B. Each successive derivative of y is equal to 0. O C. Each successive derivative of y is equal to y plus some constant C. O D. Each successive derivative of y is equal to y. Using the information in the previous step, find f₂(x,y). f₂ (x,y) = Substitute the values of h, f(xn Yn), and f₂ (XnYn) into the formula for Yn+1 Yn+1 = C n 1 1 «=[+++ 2)^• 1+ n 2n , for n = 1, 2,...
Transcribed Image Text:1 is given by the formula y = The Taylor method of order 2 can be used to approximate the solution to the initial value problem y' = y, y(0) = 1 at x = 1. Show that the approximation y obtained by using the Taylor method of order 2, with step size n The solution to the initial value problem is y=e*, so yn is an approximation of the constante. Let y'=f(x,y) and y'' = f₂(x,y). If Xn+1 = X₁ +h, then which recursive formula, for Yn+1, represents the Taylor method of order 2? h O A. Yn+1=Yn + f(xn Yn) + ¹₂ (xn-Yn) h h • + h²{x₁ + 1 = ₁ yn + · +hf/xn- in + 1/{f(xnxn)) OC. Yn+1+Yn +hf(xn+h, Yn+hf(xn Yn)) O B. Yn+1=Yn+h h² OD. Yn+1=Yn +hf(xn-Yn) + 21¹2(XnYn) In this case, what is the value of h? h= If y' = y, what can be said about each successive derivative of y? O A. Each successive derivative of y is equal to some constant C. O B. Each successive derivative of y is equal to 0. O C. Each successive derivative of y is equal to y plus some constant C. O D. Each successive derivative of y is equal to y. Using the information in the previous step, find f₂(x,y). f₂ (x,y) = Substitute the values of h, f(xn Yn), and f₂ (XnYn) into the formula for Yn+1 Yn+1 = C n 1 1 «=[+++ 2)^• 1+ n 2n , for n = 1, 2,...
Why is the equation in the problem statement true for n = 1, 2,...? O A. Raising both sides of the equation in the previous step to the power of n, results in the desired equation. O B. Substituting n = 1, 2,... into the equation in the previous step always results in a true equation. times the previous term yn OC. Each term yn +1 is always 1+ + n 2n² O D. Since the differential equation y'=y is true, the corresponding difference equation Yn+1 = Yn is also true. Making the substitution Yn+1 = Yn results in the desired equation.
Transcribed Image Text:Why is the equation in the problem statement true for n = 1, 2,...? O A. Raising both sides of the equation in the previous step to the power of n, results in the desired equation. O B. Substituting n = 1, 2,... into the equation in the previous step always results in a true equation. times the previous term yn OC. Each term yn +1 is always 1+ + n 2n² O D. Since the differential equation y'=y is true, the corresponding difference equation Yn+1 = Yn is also true. Making the substitution Yn+1 = Yn results in the desired equation.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS