Numerical Methods

Question 1

What is the mid ordinate rule

Answer 1

Integral of y b-a dx = h( y(1/2) + y(3/2) +….+ y(n-3/2) + y(n-1/2) )
Where h = b-a/ no. Of strips

Question 2

What is simpsons rule

Answer 2

1/3h ( y(0) + y(n) + 4( sum of y odds) + 2( sum of y evens) )
Where h is b-a/ no. Of strips

Question 3

What is eulers improved step by step method

Answer 3

Y(r+1) = y(r) + h/2 ( f(xr, yr) + f( xr+h, yr + hf( xr, yr))

Y(r+1) =yr +1/2( a + hf( x(r+1) , yr + a))
Where a= h(xr, yr)