Question
In: Advanced Math
Find the best weights (w0...w4) of the highest possible order finite difference formula of the form...
Find the best weights (w0...w4) of the highest possible order finite difference formula of the form f'(x) ~ w0*f(x) + w1*f(x+h) + w2*f(x+2h) + w3*f(x+3h) + w4*f(x+4h) and use Taylor series to predict the convergence order as h is decreased.
Solutions
Colby Messinger answered 4 months agoRelated Solutions
Derive a three-point formula with the highest possible order (of h) to approximate f '(a) and...
Derive a three-point formula with the highest possible order (of
h) to approximate f '(a) and f "(a), respectively, using f(a − 2h),
f(a + h), f(a + 2h).
Using the atomic weights of selected elements given below, find the formula weights for the following...
Using the atomic weights of selected elements given below, find
the formula weights for the following compounds:
Atomic weights of selected elements
Ca = 40 g moL-1, C = 12 g moL-1, O = 16 g
moL-1, H = 1 g moL-1, P = 31 g
moL-1, K = 39 g moL-1
Si = 28 g moL-1, Al = 27 g moL-1, S = 32 g
moL-1, N = 14 g moL-1
Example:
(NH4)2SO4
Element
no. of moles
Atomic...
Derive the 2nd order accurate finite difference approximation for the 1st derivative of a function at...
Derive the 2nd order accurate finite difference approximation
for the 1st derivative of a function at the data point Xo. That is,
find the coefficients a, b, c such that: af(Xo) + bf(X1) + cf(X2) =
f'(Xo) + O(h^2). (Note: there is a prime sign on the f'(Xo) at the
right side)
Rank the following in order from best (highest rate of return) to worst (lowest rate of...
Rank the following in order from best (highest rate of return)
to worst (lowest rate of return).
Investment One: 12% p.a. compounding continuously
Investment Two: 11% p.a. compounding continuously
Investment Three: 11.50% p.a. compounding semi-annually
Investment Four: 13% p.a. compounding annually
Investment Five: 12% p.a. compounding monthly
Select one:
a. The rank from highest to lowest is: 4, 1, 3, 5, 2
b. The rank from highest to lowest is: 2, 3, 5, 1, 4
c. The rank from highest...
9. Rank the following in order from best (highest rate of return) to worst (lowest rate...
9.
Rank the following in order from best (highest rate of return)
to worst (lowest rate of return).
Investment One: 12% p.a. compounding continuously
Investment Two: 11% p.a. compounding continuously
Investment Three: 11.50% p.a. compounding semi-annually
Investment Four: 13% p.a. compounding annually
Investment Five: 12% p.a. compounding monthly
Select one:
a. The rank from highest to lowest is: 4, 1, 3, 5, 2
b. The rank from highest to lowest is: 5, 1, 4, 3, 2
c. The rank from...
Find a possible formula for the trigonometric function whose values are in the following table. x...
Find a possible formula for the trigonometric function whose
values are in the following table.
x
0
2
4
6
8
10
12
y
8
2
-4
2
8
2
-4
y =
1. Find a possible formula for the trigonometric function whose values are in the following table....
1. Find a possible formula for the trigonometric function whose
values are in the following table.
X 0 2 4 6 8 10 12
Y 5 1 -3 1 5 1 -3
y=?
2. A population of rabbits oscillates 15 above and below an
average of 128 during the year, hitting the lowest value in January
(t = 0). Find an equation for the population, P, in terms
of the months since January, t.
P(t) =
What if the lowest...
Find a possible formula for the trigonometric function whose values are in the following table. x...
Find a possible formula for the trigonometric function whose
values are in the following table.
x
0
4
8
12
16
20
24
y
8
4
0
4
8
4
0
5. Find a closed-form formula for the exponential generating function for the number of strings of...
5. Find a closed-form formula for the exponential generating
function for the number of strings of length n with symbols a, b,
c, where (number of a′s) + (number of b′s) ≥ 1; and, # c′s =
even
Find the finite-difference solution of the heat-conduction problem PDE: ut = uxx 0 < x <...
Find the finite-difference solution of the heat-conduction
problem
PDE: ut = uxx 0 < x < 1, 0 < t < 1
BCs:
⇢
u(0, t) = 0
ux(1, t) = 0
0 < t < 1
IC: u(x, 0) = sin(pi x) 0 x 1
for t = 0.005, 0.010, 0.015 by the explicit method. Assume
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