quadrom - Week 8 - Romberg Algorithm - Richardson...

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Week 8 - Romberg Algorithm - Richardson Extrapolation - Gaussian quadrature
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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
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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
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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
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This note was uploaded on 10/21/2011 for the course CSCI 2031 taught by Professor Meyer during the Spring '08 term at Minnesota.

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quadrom - Week 8 - Romberg Algorithm - Richardson...

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