[其他] 差分運算與雷建德
想請問大大這兩題該如何下手
Q2.
(a) Given fi=f(xi) with x0=a, xN=b, and xi=a+hi for i=1,2,…N
where h≡(b-a)/N . Derive a finite-difference formula for an evaluation
of f"(xi) by using points of i-2,i-1,i,i+1,i+2.
(b)Redo the problem in (a) by using points of i,i+1,i+2,i+3,i+4 instead.
(c)Select some smooth functions, simple or complex, for f(x). Find numerically
the orders of accuracy of the formulas you derive in (a) and (b). Are they
out of your expectation?
此題想法是(a)題代入之後在(b)題的意義有點不太懂,(c)題圓滑函數是如何找出?
(c)題要假設常數數值分析畫出圖形嗎?
Q3
Show ci=(2(1-xi^2))/(〖(N+1)〗^2 [LN+1(xi)]^2 ) for the
Gaussian-Legendre quadrature integration method by taking advantage of the
recurrence relations of the Legendre polynomials as follow
N LN(x) = (2N-1) x LN-1(x) - (N-1) LN-2(x)
(x^2-1) LN'(x)=N x LN(x) - N LN-1(x)
此題想法是要利用高斯正交積分法,但跟雷建德遞推是如何遞推
小弟真的不太懂,想請大大們能給個意見
想法算式是:
ci=∫[ LN(x) / (x-xi) LN'(xi)] dx , [-1,1]
謝謝各位!
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※ 編輯: ksvs73010182 (61.228.35.81), 05/17/2015 00:43:30