Given theta is in [0,1] find the order of the following
method:
![Given θ E [0, 1], find the order of the method yn+1 yn + hf (tn + (1-0)hityn + (1-0)y, +1) .](http://img.homeworklib.com/images/ac433827-af87-4d69-861e-4b13f9d070f8.png?x-oss-process=image/resize,w_560)
Homework Answers
2. f6pts) A proposed multistep method is given by Yn+1 = Yn + M(h) = Yn...
2. f6pts) A proposed multistep method is given by Yn+1 = Yn + M(h) = Yn +h(Bifi + B3f3) where fk = f(yn-k, tn-k). Find Bk to maximize the order of the local error (minimize local error). Follow the example in the notes, define a = tn, F($) = f(y(s), s), rath I(h) = [** F(s) ds M(h) = h (B1F(a – h) + B3F(a – 3h)) eſh) = 1(h) – M(h) = E(0)h + E"(0)h² + (h) In the...
Please answer question #1 and write legibly. EEM is explicit euler method and IEM is implicit...
Please answer question #1 and write legibly. EEM is explicit
euler method and IEM is implicit euler method
1. We defined the Theta method: for 0 € [0, 1] Jtq+1 =t, + ; yn+1 = Yn + hof (tr; yn) + (1 - 0)f(tn+1 Yn+1)] Clearly, 0 - corresponds to the Trapezoidal rule, 0 = 1 to EEM, and 0 - o to IEM. Prove that the order of consistency of the Theta method is 1 for any
Let X1,X2,X3..Xn be iid of f(x)= theta. x^(theta-1), with x(0,1) and theta being a positive numbe...
Let X1,X2,X3..Xn be iid of f(x)= theta. x^(theta-1), with x(0,1) and theta being a positive number. Is the parameter identifiable?.Compute the maximum likelihood estimate. If instead of X1,X2,,, We observe, Y1,Y2,...Yn, where Yi=1(Xi<=0.5).What distribution does Yi follow? What is the parameter of this distribution? Compute MLE and the method of moments and Fisher information.
Let X1,X2,X3..Xn be iid of f(x)= theta. x^(theta-1), with x(0,1) and theta being a positive number....
Let X1,X2,X3..Xn be iid of f(x)= theta. x^(theta-1), with x(0,1) and theta being a positive number. Is the parameter identifiable?.Compute the maximum likelihood estimate. If instead of X1,X2,,, We observe, Y1,Y2,...Yn, where Yi=1(Xi<=0.5).What distribution does Yi follow? What is the parameter of this distribution? Compute MLE and the method of moments and Fisher information.
3. Consider the initial value problem y(t) = y, y(0) = 1. a. Write down (i.e.,...
3. Consider the initial value problem y(t) = y, y(0) = 1. a. Write down (i.e., write the formula which describes one step, Yn+1 = yn + ...) the second order Taylor method with step size h for this initial value problem. b. Write down the time stepping formula Yn+1 = Yn +... for the modified Euler method 9n+1 := yn + hf(en +3.29 + s(tn, yn)), for this initial value problem. c. What is the difference between the two...
Question 3: A random variable X has a Bernoulli distribution with parameter θ є (0,1) if...
Question 3: A random variable X has a Bernoulli distribution with parameter θ є (0,1) if X {0,1} and P(X-1)-θ. Suppose that we have nd random variables y, x, following a Bernoulli(0) distribution and observed values y1,... . Jn a) Show that EIX) θ and Var[X] θ(1-0). b) Let θ = ỹ = (yit . .-+ yn)/n. Show that θ is unbiased for θ and compute its variance. c) Let θ-(yit . . . +yn + 1)/(n + 2) (this...
3. Consider the initial value problem y'(t) = y2, y(0) = 1. a. Write down (i.e.,...
3. Consider the initial value problem y'(t) = y2, y(0) = 1. a. Write down (i.e., write the formula which describes one step, Yn+1 = yn + ...) the second order Taylor method with step size h for this initial value problem. b. Write down the time stepping formula Yn+1 = Yn +... for the modified Euler method h Yn+1 := yn + hf(tn + h 2:9 » Yn + 5 f (tnYn)), for this initial value problem. c. What...
5. Consider the following second order explicit Runge-Kutta scheme: k=hf(an, Yn) k2 = hf(2, +h, yn...
5. Consider the following second order explicit Runge-Kutta scheme: k=hf(an, Yn) k2 = hf(2, +h, yn +ki) Yn+k2. Yn+1 (a) Express the following ordinary differential equation and initial conditions as a sys- tem of first order equations: y(1)=1, /(1) 3. (b) Use the second order explicit Runge-Kutta scheme with one step to compute an approximation to y(1.2).
5. Consider the following second order explicit Runge-Kutta scheme: k=hf(an, Yn) k2 = hf(2, +h, yn +ki) Yn+k2. Yn+1 (a) Express the following...
1. Let A= {0,1}2 U... U{0,1}5 and let < be the order on A defined by...
1. Let A= {0,1}2 U... U{0,1}5 and let < be the order on A defined by (s, t) E< if and only if s is a prefix of t. (We consider a word to be a prefix of itself.) (a) Find all minimal elements in A. (Recall that an element x is minimal if there does not exist y E A with y < x.) (b) Are 010 and 01101 comparable? 2. Give an example of a total order on...
2. f6pts) A proposed multistep method is given by Yn+1 = Yn + M(h) = Yn +h(Bifi + B3f3) where fk = f(yn-k, tn-k). Find Bk to maximize the order of the local error (minimize local error). Follow the example in the notes, define a = tn, F($) = f(y(s), s), rath I(h) = [** F(s) ds M(h) = h (B1F(a – h) + B3F(a – 3h)) eſh) = 1(h) – M(h) = E(0)h + E"(0)h² + (h) In the...
Please answer question #1 and write legibly. EEM is explicit
euler method and IEM is implicit euler method
1. We defined the Theta method: for 0 € [0, 1] Jtq+1 =t, + ; yn+1 = Yn + hof (tr; yn) + (1 - 0)f(tn+1 Yn+1)] Clearly, 0 - corresponds to the Trapezoidal rule, 0 = 1 to EEM, and 0 - o to IEM. Prove that the order of consistency of the Theta method is 1 for any
3. Consider the initial value problem y(t) = y, y(0) = 1. a. Write down (i.e., write the formula which describes one step, Yn+1 = yn + ...) the second order Taylor method with step size h for this initial value problem. b. Write down the time stepping formula Yn+1 = Yn +... for the modified Euler method 9n+1 := yn + hf(en +3.29 + s(tn, yn)), for this initial value problem. c. What is the difference between the two...
Question 3: A random variable X has a Bernoulli distribution with parameter θ є (0,1) if X {0,1} and P(X-1)-θ. Suppose that we have nd random variables y, x, following a Bernoulli(0) distribution and observed values y1,... . Jn a) Show that EIX) θ and Var[X] θ(1-0). b) Let θ = ỹ = (yit . .-+ yn)/n. Show that θ is unbiased for θ and compute its variance. c) Let θ-(yit . . . +yn + 1)/(n + 2) (this...
3. Consider the initial value problem y'(t) = y2, y(0) = 1. a. Write down (i.e., write the formula which describes one step, Yn+1 = yn + ...) the second order Taylor method with step size h for this initial value problem. b. Write down the time stepping formula Yn+1 = Yn +... for the modified Euler method h Yn+1 := yn + hf(tn + h 2:9 » Yn + 5 f (tnYn)), for this initial value problem. c. What...
5. Consider the following second order explicit Runge-Kutta scheme: k=hf(an, Yn) k2 = hf(2, +h, yn +ki) Yn+k2. Yn+1 (a) Express the following ordinary differential equation and initial conditions as a sys- tem of first order equations: y(1)=1, /(1) 3. (b) Use the second order explicit Runge-Kutta scheme with one step to compute an approximation to y(1.2).
5. Consider the following second order explicit Runge-Kutta scheme: k=hf(an, Yn) k2 = hf(2, +h, yn +ki) Yn+k2. Yn+1 (a) Express the following...
1. Let A= {0,1}2 U... U{0,1}5 and let < be the order on A defined by (s, t) E< if and only if s is a prefix of t. (We consider a word to be a prefix of itself.) (a) Find all minimal elements in A. (Recall that an element x is minimal if there does not exist y E A with y < x.) (b) Are 010 and 01101 comparable? 2. Give an example of a total order on...
Most questions answered within 3 hours.
-
Steven can afford car payments of $300 a month for 72 months.
The bank will lend...
asked 10 minutes ago -
Embedded
System..
1.
Analyze
the instruction
sets below.
LDR R1, [R0,
#0x08]
SUB R1, R1,
R2,...
asked 14 minutes ago -
Use proper sentence structure to communicate clearly.
Choose the correct sentence structure in each of the...
asked 14 minutes ago -
There are investors who claim they only invest in companies with
great products and outstanding management,...
asked 17 minutes ago -
what is employee/ employer relations ?
why is Employee/ Employer relation is important in the context...
asked 35 minutes ago -
Explain the relationship between tests of acquisition and
payment cycle and tests of accounts payable. Give...
asked 34 minutes ago -
A hot-air balloon is descending with a velocity of (−2.00m/s)y^.
A champagne bottle is opened to...
asked 52 minutes ago -
1. When a nearsighted person looks at an object that is in the
distance with their...
asked 2 hours ago -
QUESTION 8
Both of these statements will store the same value in the
variable $number
$number...
asked 2 hours ago -
The price of 1 lb of potatoes is $1.75. If all the potatoes sold
today at...
asked 3 hours ago -
Garcia Company issues 20.00%, 15-year bonds with a par value of
$470,000 and semiannual interest payments....
asked 3 hours ago -
In C++ Programming, Try using loops only.
This lab demonstrates the use of the While Loop...
asked 4 hours ago