I have now typed something in Python.
for k = 2, xbar = pi/2, and x =[pi/2-0.2 , pi/2-0.1, pi/2, pi/2 + 0.1, pi/2 + 0.2]
I get the results:
C = [-8.33333333, 133.33333333, -250. , 133.33333333, -8.33333333]Can someone with MATLAB license please verify this result. I will be...
In a self learning project I am fooling around book https://faculty.washington.edu/rjl/fdmbook/
I want to do some of the computation myself to better understand the concepts but the book is Matlab based and Matlab is too expensive.
Does anyone by any chance have some of the codes provided by...
For Initial Value problems I want to implement an ODE solver for implicit Euler method with adaptive time step and use step doubling to estimate error. I have found some reading stuff about adaptive time step and error estimation using step doubling but those are mostly related to RK methods. I...
I have lately been working with Numerical Analysis and I am using Finite Difference Methods for Ordinary and Partial Differential Equations by Randall J. LeVeque. It was recommended to me by a friend of mine (physicist)
https://epubs.siam.org/doi/book/10.1137/1.9780898717839?mobileUi=0&...
This is not so much a "Homework" question I am just giving an example to ask about a specific topic.
Homework Statement
Is ##f(t,y)=e^{-t}y## Lipschitz continuous in ##y##
Homework Equations
I don't really know what to put here. Here is the definitions...
You're right that I am not quite certain about there terminology. I am using the textbook by Levee: Finite Difference Methods for Ordinary and Partial DE.
But the terminology is not clear for me and that is Exactly what I am asking about. My answer to the question is: (a+h*0), (a+h*1), ... and...
Homework Statement
Determine the Finite Difference Method stencil for approximating a second derivative u''(x) at a discrete set of nodes with maximum accuracy for stencil of sizes (0,4) (off-centered).
My questions:
I think I am able to answer the question I am just not sure about what is...
Homework Statement
I am asked to show that E[\exp(a*W_t)]=\exp(\frac{a^2t}{2})
Let's define: Z_t = \exp(a*W_t)
W_t is a wiener process
Homework Equations
W_t \sim N(0,\sqrt{t})
The Attempt at a Solution
I want to use the following formula.
if Y has density f_Y and there's a ral function g...
Homework Statement
The number of busy lines in a trunk group (Erlang system) is given by a truncated Poisson distribution. I am asked to generate values from this distribution by applying the Metropolis-Hastings algorithm.
Homework Equations
The distribution is given in the attached picture...
Homework Statement
I look at the distribution ##(Y_1,Y_2,...,Y_n)##
where
##Y_i=μ+(1+φ x_i)+ε_i## where ##-1<φ<1## and ##-1<x_i<1## . x's are known numbers. ε's are independent and normally distributed with mean 0 and variance 1.
I need to find the the maximum likelihood estimator for μ and...
I try to find out how to minimize functions i R by using nlm function:
> f<-function(x,y){x^2+y^2+10-5*x-y}
> nlm(f,0.1,0.1)
That only gives me an estimate for x. How would write the code to get x and y?
They are discrete and I was wrong saying that they are independent.
I know I have to do some work before, but I brought it because I'm totally stuck. I think my problem is that in this course our textbook only have examples for one variable and not multi. That confuses me.
Homework Statement
https://dl.dropboxusercontent.com/u/17974596/Sk%C3%A6rmbillede%202016-02-02%20kl.%2007.35.26.png
I want to find variance matrix and expected variance vector of Y=(Y1,Y2). Y1 and Y2 are independant. Γ is the gamma function and ϒ is a known parameter. λ1>0 λ2>0 and ϒ>0...