{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

quadrom - Week 8 Romberg Algorithm Richardson Extrapolation...

Info icon This preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Week 8 - Romberg Algorithm - Richardson Extrapolation - Gaussian quadrature
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Romberg Algorithm R(n,0) = 0.5*∑ h/2 n [f(x i ) + f(x i+1 )] R(n,m) = R(n,m-1) + R(n,m-1) - R(n-1,m-1) 4 m -1 i=0 n-1 R(0,0) R(1,0) R(2,0) R(1,1) R(2,1) R(2,2) ∫tan(x) 0 1 R(0,0) = 0.5*(1*[tan(0) + tan(1)]) R(1,0) = 0.5*(.5*[tan(0)+2*tan(.5)+tan(1)]) R(2,0) = 0.5*(.25*[tan(0)+2*tan(.25) 2*tan(.5)+2*tan(.75)+tan(1)]) R(1,1) = R(1,0) + [R(1,0)-R(0,0)]/3 R(2,1) = R(2,0) + [R(2,0)-R(1,0)]/3 R(2,2) = R(2,1) + [R(2,1)-R(1,1)]/15 .7787 .6625 .6279 .6164 .6159 .6237
Image of page 2
Romberg Algorithm R(n,0) = 0.5*∑ h/2 n [f(x i ) + f(x i+1 )] R(n,m) = R(n,m-1) + R(n,m-1) - R(n-1,m-1) 4 m -1 i=0 n-1 R(0,0) R(1,0) R(2,0) R(1,1) R(2,1) R(2,2) ∫tan(x) 0 1 R(0,0) = 0.5*(1*[tan(0) + tan(1)]) R(1,0) = 0.5*(.5*[tan(0)+2*tan(.5)+tan(1)]) .7787 .6625
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Romberg Algorithm R(n,0) = 0.5*∑ h/2 n [f(x i ) + f(x i+1 )] R(n,m) = R(n,m-1) + R(n,m-1) - R(n-1,m-1) 4 m -1 i=0 n-1 R(2,0) R(1,1) R(2,1) R(2,2) ∫tan(x) 0 1 R(2,0) = 0.5*(.25*[tan(0)+2*tan(.25) 2*tan(.5)+2*tan(.75)+tan(1)]) .7787 .6625 .6279
Image of page 4
Romberg Algorithm R(n,0) = 0.5*∑ h/2 n [f(x i ) + f(x i+1 )] R(n,m) = R(n,m-1) + R(n,m-1) - R(n-1,m-1) 4 m -1 i=0 n-1 R(1,1) R(2,1) R(2,2) ∫tan(x) 0 1 .7787 .6625 .6279 R(1,1) = R(1,0) + [R(1,0)-R(0,0)]/3 R(2,1) = R(2,0) + [R(2,0)-R(1,0)]/3 .6237 .6164
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Romberg Algorithm R(n,0) = 0.5*∑ h/2 n [f(x i ) + f(x i+1 )] R(n,m) = R(n,m-1) + R(n,m-1) - R(n-1,m-1) 4 m -1 i=0 n-1 R(2,2) ∫tan(x) 0 1 .7787 .6625 .6279 .6237 .6164 R(2,2) = R(2,1) + [R(2,1)-R(1,1)]/15 .6159 Real answer: 0.61562647
Image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern