Please upload your solutions in pdf. 1. Solve the initial value problem

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

solve the following Runge-Kutta Method

 

Please upload your solutions in pdf.
1. Solve the initial value problem
2,1/2
y = (3x +y) -y
2
with y(2) = 0 and h = 0.2 over the interval 2sxs 3. Solve the equation again by analytical method and compare their results (i.e. analytical vs
numerical).
2. Here is how to use the second-order Runge-Kutta Method with the same given as in fourth-order:
Solve for k, and k,.
ki = hf (xn, Yn)
k2 = hf(xn + h,yn + k1)
and then, solve for the next value of y:
Yn+1 = Yn +(kı + k2) for n = 1, 2, ...
where
* = X + nh.
Now, try to sov
2 1/2
y = xy/(x +y)
the initial value problem
2
with y(1) = 1 and h = 0.2 over the interval 1 sxs 2 using second-order Runge-Kutta Method. Solve the equation again by fourth-order Runge-Kutta
Method and compare their results (i.e. 2nd order vs 4th order).
Transcribed Image Text:Please upload your solutions in pdf. 1. Solve the initial value problem 2,1/2 y = (3x +y) -y 2 with y(2) = 0 and h = 0.2 over the interval 2sxs 3. Solve the equation again by analytical method and compare their results (i.e. analytical vs numerical). 2. Here is how to use the second-order Runge-Kutta Method with the same given as in fourth-order: Solve for k, and k,. ki = hf (xn, Yn) k2 = hf(xn + h,yn + k1) and then, solve for the next value of y: Yn+1 = Yn +(kı + k2) for n = 1, 2, ... where * = X + nh. Now, try to sov 2 1/2 y = xy/(x +y) the initial value problem 2 with y(1) = 1 and h = 0.2 over the interval 1 sxs 2 using second-order Runge-Kutta Method. Solve the equation again by fourth-order Runge-Kutta Method and compare their results (i.e. 2nd order vs 4th order).
Expert Solution
steps

Step by step

Solved in 6 steps with 11 images

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,