use the least-squares collocation method with trigonometric basis fuctions sin(n

Question

use the least-squares collocation method with trigonometric basis fuctions sin(n*pie*x/2) (n = 1,2,3,4,5,6,7)

to solve the following third order differential equation

4y''' + 6y'' + 3y' +7y = 2 + cos(pie * x)

x is from 0 to 2

with conditions

f(0) = 0

f(1) = 4

f(2) = 0

ok I don't need it to be solved per say, I don't understand differentials, but apparently this can be solved with matrix operations and I can do that, so what i need to get the values for y is construct and operate on a number of matrices. What I need to know is

1) what is a basis function, and what am i supposed to do with it?

2) what matrices do i need to construct and How do i construct them

3) What operations do I have to do on those matrices in order to obtain a value for y

4) How to do it with the conditions presented in the question

Please Walk me through with an explenation on what i need to do in order to do this

Explanation / Answer

what i suggest is dat u should solve these equation using complex notation.

let me tell u wat a basis function is-

In mathematics, a basis function is an element of a particular basis for a function space. Every continuous function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors.

giving credits to the particular place from wer i understood the above thing,u mite like to refer to-

http://www.janmagnus.nl/misc/mdc2007-3rdedition

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.