In mathematics and computational science, the Euler method (also called forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who treated it in his book Institutionum calculi integralis (published 1768–1870).The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size.
The Euler method often serves as the basis to construct more complex methods, e.g., predictor–corrector method.
I want to know which statistical method to use for the below problem.
Suppose I have the revenue data of 5 companies in the same industry. And, also the market share of the industry. I calculated the ratio of all against each other. Now, with the above calculation, i want to find out which among...
I have been interested in (the concept of) large frame industrial combustion turbine supercharging since the early 90's. However, although I believe the concept has merit and has been done successfully in at least one location nearly 3 or 4 decades ago, the concept has not evolved since...
You can use transfer matrix method for 2d Ising model. Is there a list of models for which this method could be of use. Such as classical Heisenberg perhaps? Or Potts?
Hi!, I'm working on a personal project: Solve the heat equation with the semi discretization method, using my own Mathematica's code, (W. Mathematica 9). The code:
I'm having problems with the variable M (the number of steps). It works with M=1-5, but no further, I do not know what's going...
Homework Statement
I am trying to create a MATLAB program that propagates the solar system when given initial velocity and position. I have successfully implemented a Runge-Kutta 4th order integrator but would like to see the difference when moving to an adaptive time step method. I think my...
Homework Statement
Let ##X_1, X_2, ..., X_n## be a random sample from ## f_θ=2x/θ^2## , ##0≤x≤θ##.
Find a maximum likelihood estimator for θ. Find the method of moment estimator for θ.
The Attempt at a Solution
I have already found that the MLE is max{##x_i##}. I just need to find the...
Let $f(z)=\frac{(z^2+1)^2}{(z^2+2z+2)^3}$ . Evaluate the contour integral of $f'(z)/f(z)$ around the circle $|z|=4$?
How do I do this without having to find $f'(z)$?
Thanks
i have a question, when i put a oil seal in a housing, should i put grease between the housing and the oil seal? because that is more easy to out in.
Can explain the theory to me please?
Definition/Summary
CORDIC (digit-by-digit method, Volder's algorithm) (stands for COordinate Rotation DIgital Computer) is a simple and efficient algorithm to calculate hyperbolic and trigonometric functions. It is commonly used when no hardware multiplier is available as the only operations...
When deriving the Runge-Kutta Method to solve y'=f(x) we need to use Taylor expansion. Hence we need to differentiate the function many times.
y'(x)=f(y(x))
y''(x)=f'(y(x))y'(x) = f'(y(x))f(y(x))
y''' = f''(y(x))(f(y(x)),y'(x)) + f'(y(x))f'(y(x))y'(x)
I can understand the second...
Hi
I want to estimate divergence of water vapor flux in atmosphere with NCEP/NCAR data
I have the equations for that and i want the algorithms to implement it for NCEP/NCAR data.
I have a paper with algorithms for ECMWF data. Can i take this? or it required new algorithms for my data
This isn't really a homework question, but may be similar to a typical example problem so I posted it here.
Homework Statement
I want to find the max and min dot product of a 3d vector and all points in a sphere constrained by angles in spherical coordinates.
Homework Equations
A point...
Hello,
Can someone show me how the inverse Phasor transform of the sum of individual Phasors of sinusoidal functions of the same frequency is the sum of the sinusoids? I could not find any rigorous proof and help appreciated.
Thanks.
use euler's method with step size 0.1 to estimate y(0.5), where y(x) is the solution of the initial-value problem y'=y(x+1), y(0)=1. round your answer to four decimal places.
this is all I've done so far
$y'=y(x+1)$
$y(0)=1$
$h=0.1$
$x_{0}=0$
$y_{0}=1$
$x_{1}=x_{0}+h=0+0.1=0.1$...
I'm doing a practice problem I found online, and I get a solution, but I think it should have a sine term in it. I looked up the solution, and most sites say to use variation of parameters, but is it possible to use the method of undetermined coefficients?
The problem is as follows: y'' + 4y...
Hello,
Been a while since I posted on here, nice to be back :) .
I just want some pointers as to the methodology for an impact load case that I'm looking at. I've attached a very basic sketch of a trolley which is traveling at a known velocity and impacts a rigid structure at it's base.
What...
When using Euler's method of integration, applied on a stochastic differential eq. :
For example - given
d/dt v=−γvΔt+sqrt(ϵ⋅Δt)Γ(t)
we loop over
v[n+1]=v[n]−γv[n]Δt+sqrt(ϵ⋅Δt)Γn.
(where −γv[n] is a force term, can be any force and Γn is some gaussian distributed random variable. ) .
Then if...
I need to convert 12.5 MPa·mm1/2 into MPa.m1/2.
I am unsure on how to do this, my two guesses are as follows:
1. (12.5) / ( 1 / 10001/2) = 395.28 MPa.m1/2
2. (12.5) / (12.5 / 10001/2) = 31.62 MPa.m1/2
Is either of those correct? Thanks!
Hi all, I'm doing a project on the finite elements method and am struggling to understand a part of it.
I have defined the hat functions as:
\[
\phi_i(x) =
\begin{cases}
\frac{x-x_{i-1}}{h} & \text{if } x_{i-1}\leq x<x_i \\
\frac{x_{i+1}-x}{h} & \text{if } x_i\leq x<x_{i+1}\\
0 &...
Homework Statement
Use Newton's method with x1 = 1 to find the root of the equation x3 - x = 1 to correct six decimal places.
Do the question again with x1 = 0.6
Do the question again with x1 = 0.57
You probably need to do it in an excel sheet. With each try, it takes longer to...
Hi all,
I need help with numerical solution of motion equation.
From the numerical point of view and in the real of the finite element method, which method is recommended for the solution of damped ( proportional damping) linear motion equation?
I have been trying three common methods; Modal...
hi there; I need some help with the following formulas
In the interaction picture.
##\frac{d}{dt}\rho(t)=\frac{1}{i\hbar}[V(t),\rho(t)]## (1)
Then
##\rho(t+\Delta t) = \rho(t)+\frac{1}{i\hbar}\int_t^{t+\Delta t} dt' [V(t'),\rho(t')]## (2)
This equation can be iterated. and...
Hi all,
The plastic flow rule for large strains in a continuum medium can be written as :
-\dfrac{1}{2} \Big ( \dfrac{d}{dt}(F_p^{-1} ). ^t F_p^{-1} + F_p^{-1} . ^t \dfrac{d}{dt} ( F_p^{-1} ) \Big)= \lambda F^{-1} \dfrac{\partial f}{\partial \tau} F F_p^{-1} . ^t F_p^{-1}
where F_p is the...
I am an upcoming freshman. I will major in engineering. When applying to the school I chose mechanical because of its "versatility and stability in the job market." (I don't fully understand the meaning of these phrases; I get my knowledge from anecdotal experience when browsing forums). I may...
I am trying to solve 3 non-linear system of 3 variables using the Newton-raphson method in matlab. Here are the 3 non-linear equations:
\begin{equation} c[\alpha I+ k_f+k_d+k_ns+k_p(1-q)]-I \alpha =0 \end{equation}
\begin{equation} s[\lambda_b c P_C +\lambda_r (1-q)]- \lambda_b c P_C =0...
The picture shows the potential due to ring charge.
Please show the full steps of deriving the equation of electrical potential. I don't know how to start at all.
NOTE:
The electric potential of the revolving symmetrical ring electric charge related to the axis z as depicted in the diagram...
I am trying to solve 3 non-linear system of 3 variables using the Newton-raphson method in matlab. Here are the three equations:
\begin{equation} c[\alpha I+ k_f+k_d+k_ns+k_p(1-q)]-I \alpha =0 \end{equation}
\begin{equation} s[\lambda_b c P_C +\lambda_r (1-q)]- \lambda_b c P_C =0 \end{equation}...
Hey! :o
I have to solve the following hyperbolic system of equations using the method of characteristics:
$$\left.\begin{matrix}
\frac{\partial{u_1}}{\partial{t}}+\frac{\partial{u_1}}{\partial{x}}+x^2 \frac{\partial{u_2}}{\partial{x}}=0\\
\frac{\partial{u_2}}{\partial{t}}+t^2...
Just doing the Washer Method for now, once that's sorted out I'm going to see if I can do the Shell Method. I just want to be sure I'm doing this right here.
That's x=0, y=2, y=5-x
This is around the X-Axis.
R(y) = 5+y, r(y)=2
Assuming that part is at least correct. The integral goes from...
I don't need the answers or the problems worked out I'm asking something more basic. This is just an example problem.
y=\sqrt(x),y=0, x=3
a) Around the x-axis
R(x)=\sqrt{x}, r(x)=0
I understand the R to be the value fathers from the x-axis, and the r value to be the closer one to the...
I'm an intro calc-based physics instructor, and recently uncovered some vagueness, or maybe errors (?), with my recipe. Can you please comment on the following?
Question 1: Loop Currents - MY RECIPE:
"Determine # of loop currents by connecting each circuit junction once, and only once, to a...
Y=x^(2/3) and y=x^2 rotated about the x=4.
First I equate the equations giving me x=0,-1,1. The problem is I have exactly 2 graphs that are symmetric in respect to the y axis. N I have not encountered a problem in stewart dealing with this.
I know that the volume on the right side of the...
Homework Statement
Simplify ##d(log(x^2 + y^2) − z^3)##
Homework Equations
the derivative?
The Attempt at a Solution
The instruction says to simplify. In a similar problem I ended up using the d(a(b-c))= da d(b-c). I am not sure how to deal with the log and only found formulas...
consider the following LMM
$$y_n-\frac{3}{2}y_{n-1}+\frac{1}{2}y_{n-2}=h(\frac{1}{2}f_n+\frac{1}{4}f_{n-1}-\frac{1}{4}f_{n-2})$$
which is applied to the initial value problem $$y'(t)=y(t),0\leq{t}\leq{1}\\ and\\ y(0)=1$$
How do i find an expression for $$y_n$$, if the starting values are...
Suggest how to solve Poisson equation
\begin{equation}
σ ∇^2 V = - I δ(x-x_s) δ(y-y_s) δ(z-z_s) \nonumber
\end{equation}
by using the boundary integration method to calculate the potential $V(r,z)$ with the help of changing the Poisson equation into cylindrical polar co ordinates?
Where V is...
There are various kinds of approximation methods in band theory. In my opinion, Bloch theorem implies the existence of energy band. From nearly-free electron approximation or tight binding method, we can calculate the energy band. They can tell us the information of band gap and band width...
This problem has a lot of calculations from the beginning so i have skipped to the part i am stuck with and tried to include relevant information, apologies if i have missed anything. Assume all working is correct as i was given the answers.
After carrying out the stiffness matrix method I am...
Homework Statement
Hi,guys I have a example, i understand almost everything but i have problems understanding some steps.
Example:
2u't+3u'x=0,x\inR,t>0,u(x,0)=sin(x),u=u(x,y)
The Attempt at a Solution
I rewrite the example
(1)2u't+3u'x=u's
(2)u'tt's+u'xx's=u's
From comparing (1)...
Hi:
I have been working in this Project for a while now and I would like to share the results with you. Still needs some improvements; but it appears to be working fine so far. Please let me know your suggestions and ideas.
Thanks.
Please help me with this astronomy problem. I am supposed to calculate the smallest planet that is detectable with the transit method, given a signal to noise ratio and a star's radius:
Suppose the star is seen at its distance D with a signal to noise ratio of S/N = 10^4. This means that in...
Hello,
I have a polynomial of order n and I want to find all it's roots with bisection method. Is it possible? I already wrote an algorithm to find a root and it's works nice for finding one of it's roots, but what about others?
Nikola
Homework Statement
I would like to solve a 2nd Order Differential Equation using the Improved Euler Method. The 2nd ODE is a Mass-Spring-Damper equation. I tried coming up with an solution for the Improved Euler Method, but not entirely sure. Can you help me and have a look if this is correct...
Homework Statement
For polynomials f(x),g(x) of degree d = 2(r−1)−1, check that multiplying f(x) and g(x) by the Karatsuba method requires 3(r-1) multiplications in the field F.
Homework Equations
You can can more clearly see problem on page 383 #10...
Integral[(dx/(ex+1)]
Here’s my method:
If
x = -Ln(u)
Then
dx = -du/u;
ex = 1/u;
u = e-x;
Substituting in the integral we get:
Integral[(-du/u)/((1/u)+1)] = -Integral[du/(1+u)]
Solving the integer in terms of u:
-Ln|1+u|+C
Substituting x in the result:
-Ln|1+e-x|+C
Sorry that i didn't use the...