Differential Equations Solutions 139

Differential Equations Solutions 139 - t so that f ( t ) =...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
149 CHALLENGE 24.5. Using the Lagrange form of the interpolating polynomial, we can write p ( f )= L 1 ( f ) t 1 + L 2 ( f ) t 2 + L 3 ( f ) t 3 , where L 1 ( f )= ( f f 2 )( f f 3 ) ( f 1 f 2 )( f 1 f 3 ) , L 2 ( f )= ( f f 1 )( f f 3 ) ( f 2 f 1 )( f 2 f 3 ) , L 3 ( f )= ( f f 1 )( f f 2 ) ( f 3 f 1 )( f 3 f 2 ) . It is easy to verify that L j ( f j )=1and L j ( f k )=0if j ± = k . Therefore, p ( f 1 )= t 1 , p ( f 2 )= t 2 ,and p ( f 3 )= t 3 , as desired. Now, we want to estimate the value of
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: t so that f ( t ) = 0, and we take this estimate to be p (0). We calculate: L(1) = f(2)*f(3)/((f(1)-f(2))*(f(1)-f(3))); L(2) = f(1)*f(3)/((f(2)-f(1))*(f(2)-f(3))); L(3) = f(1)*f(2)/((f(3)-f(1))*(f(3)-f(2))); testimated = L*t;...
View Full Document

Ask a homework question - tutors are online