Using The Method Of Undetermined Coefficients Derive An Approximation Formula For The First Derivative Over The Stencil 1 (70.69 KiB) Viewed 30 times
Using the method of undetermined coefficients, derive an approximation formula for the first derivative over the stencil with nodes {10, 20 + h, xo + 2h} 20th 20+2h 20 <=10+h in the form 6 f'(T) 20f(x0) + a f(20 +h) + a2f(20 +2h) at the place x = 10 + A. As a function of r, determine po(x) = and pi(2) = and P2(2) (use notation xo for 2o) 6 B. Determine po co + and ps(+0+*) 6 h = and (20 + 4) = p2 C. Determine: po(20) = D. Determine: po(20+h) = E. Determine: po(20 + 2h) = and p1(20) = and p2(20) = and pı(20 + h) and p2(10 + h) = and pı(to + 2h) = and p2(20 + 2h) = 6 F. Determine: po( 20 + and ph (20 + 3) - ah and pato + o ps($ +- = G. Using the method of undetermined coefficients the linear system of equations are From Po: ao+ 02 21+ From Pu: ao+ a1+ 02 Q1 + From P2 20+ 02 H. Solve the above system to get approximation + aof() + f(20 +h) + a2f(10 + 2h) = f(20)+ f(20+h)+ f(20 + 2h)
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+- = G. Using the method of undetermined coefficients the linear system of equations are From Po: ao+ 02 21+ From Pu: ao+ a1+ 02 Q1 + From P2 20+ 02 H. Solve the above system to get approximation + aof() + f(20 +h) + a2f(10 + 2h) = f(20)+ f(20+h)+ f(20 + 2h)