Question 6:
Evaluate S (1+r3
S*(1+) dx by using the
Trapezoidal rule divide the interval
[0,2] into 4 equal sub-intervals
5.29
6.25
6.76
5.76
Answers
Answered by
0
Answer:
> 5. Numerical Integration
Review of Interpolation
Find pn(x) with pn(xj ) = yj , j = 0, 1, 2, . . . , n. Solution:
pn(x) = y0`0(x) + y1`1(x) + . . . + yn`n(x), `k(x) = Qn
j=1,j6=k
x−xj
xk−xj
.
Theorem
Let yj = f(xj ), f(x) smooth and pn interpolates f(x) at
x0 < x1 < . . . < xn. For any x ∈ (x0, xn) there is a ξ such that
f(x) − pn(x) = f
(n+1)(ξ)
(n + 1)! (x − x0)(x − x1). . .(x − xn)
| {z }
ψ(x)
Example: n = 1, linear:
f(x) − p1(x) = f
00(ξ)
2
(x − x0)(x − x1),
p1(x) = y1 − y0
x1 − x0
(x − x0) + y0.
5. Numerical Integration
Similar questions