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The finite difference method transforms the ordinary differential equation in a system of linear equations of the form with k=1,2,...,(n−1) , h=1/n, y0=0 and yn=5 . Knowing this, make n=5 and assemble the associated linear system. Then solve numerically using some iterative method and compare the numerical solution with the exact analytical solution y(x)=x^4+4x . So do the same for n=10 and comment on what you observed.

The finite difference method transforms the ordinary differential equation in a system of linear equations of the form with k=1,2,...,(n−1) , h=1/n, y0=0 and yn=5 . Knowing this, make n=5 and assemble the associated linear system. Then solve numerically using some iterative method and compare the numerical solution with the exact analytical solution y(x)=x^4+4x . So do the same for n=10 and comment on what you observed.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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The finite difference method transforms the ordinary differential equation

in a system of linear equations of the form


with k=1,2,...,(n−1) , h=1/n, y0=0 and yn=5 .

Knowing this, make n=5 and assemble the associated linear system. Then solve numerically using some iterative method and compare the numerical solution with the exact analytical solution y(x)=x^4+4x . So do the same for n=10 and comment on what you observed.

 

 

code with python.

(2 – k²h³)yk-1 – 4(1 + 2kh³)y¼ + (2 + k²h³ )yk+1 = 0
Transcribed Image Text:(2 – k²h³)yk-1 – 4(1 + 2kh³)y¼ + (2 + k²h³ )yk+1 = 0
у+x?у - 4ху %3D 0, х€[0, 1] У(О) %3D 0, у(1) %3D 5
Transcribed Image Text:у+x?у - 4ху %3D 0, х€[0, 1] У(О) %3D 0, у(1) %3D 5
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