Method Definition and 1000 Threads

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...

The three non-linear equations are given by \begin{equation} c[(6.7 * 10^8) + (1.2 * 10^8)s+(1-q)(2.6*10^8)]-0.00114532=0 \end{equation} \begin{equation} s[2.001 *c + 835(1-q)]-2.001*c =0 \end{equation} \begin{equation} q[2.73 + (5.98*10^{10})c]-(5.98 *10^{10})c =0 \end{equation} Using...

The three non-linear equations are given by \begin{equation} c[(6.7 * 10^8) + (1.2 * 10^8)s+(1-q)(2.6*10^8)]-0.00114532=0 \end{equation} \begin{equation} s[2.001 *c + 835(1-q)]-2.001*c =0 \end{equation} \begin{equation} q[2.73 + (5.98*10^{10})c]-(5.98 *10^{10})c =0 \end{equation} Using 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...

What is the Lagrange Mesh method?

Hey I don't understand this backward euler solution, in particular why the f(y,t+h) is equal to y(t+2)

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...

Hi, I just want to know should I only use counts in tube3 to estimate microbial number, or the average of tube2 and tube3 estimation. Thank you!

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...

Consider the integral \begin{equation} I_n(x)=\int^{2}_{1} (log_{e}t) e^{-x(t-1)^{n}}dt \end{equation} Use Laplace's Method to show that \begin{equation} I_n(x) \sim \frac{1}{nx^\frac{2}{n}} \int^{\infty}_{0} \tau^{\frac{2-n}{n}} e^{-\tau} d\tau \end{equation} as x\rightarrow\infty...

Consider the integral \begin{equation} I_n(x)=\int^{2}_{1} (log_{e}t) e^{-x(t-1)^{n}}dt \end{equation} Use Laplace's Method to show that \begin{equation} I_n(x) \sim \frac{1}{nx^\frac{2}{n}} \int^{\infty}_{0} \tau^{\frac{2-n}{n}} e^{-\tau} d\tau \end{equation} as $x\rightarrow\infty$. where...

Consider the integral \begin{equation} I(x)=\int^{2}_{0} (1+t) \exp\left(x\cos\left(\frac{\pi(t-1)}{2}\right)\right) dt \end{equation} Use Laplace's Method to show that \begin{equation} I(x) \sim \frac{4\sqrt{2}e^{x}}{\sqrt{\pi x}} \end{equation} as $x\rightarrow\infty$. => I have tried using...

what method should i use? i tried u = x - 4 du = dx i can't continue. enlighten me please

A predictor-corrector method for the approximate solution of y'=f(t,y) uses \begin{equation} y_{n+1}-y_{n}=hf_{n} \tag P \end{equation} as predictor and \begin{equation} y_{n+1}-y_{n}=\frac{h}{2}(f_{n+1}-f_{n}) \tag C \end{equation} IF (P) and (C) are used in PECE mode on the...

Hi! I'm stuck on a very basic problem while trying to design a product. Basically, I need to know how to calculate the gear ratios, pitch, motor specs etc for two rack and pinion mechanisms- one horizontal and one vertical. The pinion moves along the rack in both situations. Mass to be moved-...

Homework Statement What Hybrid Methods are used for solving linear equations and how are they advantageous to classic methods? Homework Equations The Attempt at a Solution Well I assume that more robust methods such as bisection would be combined with Newtons or secant which are...

Homework Statement Name disadvantages of the Successive Method vs Newtons for solving nonlinear equations? Homework Equations The Attempt at a Solution I went all through the textbook and this is all I could find on the successive method disadvantages but these are not compared to...

How do you determine if the two expressions are equivalent using the subtraction method?$$\frac{2x^3+7x^2-5x-6}{x+1} - [(2x^2+5x-10) + \frac{4}{x+1}] $$ The textbook says that they're equivalent. I know that, using the subtraction method, they have to equal 0 in order to be equivalent. But, I'm...

Homework Statement Determine the force in members BF, BG, and AB, and state if the members are in tension or compression. Homework Equations Method of sections The Attempt at a Solution Now I cut the sections FB, BG and BA... I took the lower end. I now have three unknowns. I...

Hello everyone, I have the following question: Show without using the simplex method that x1=5/26, x2=5/2, x3=27/26 is an optimal solution to the following LPP. Maximize z=9x1+14x2+7x3 subject to 2x1+x2+3x3<= 6 5x1+4x2+x3<= 12 12x2 <= 5 x1,x2,x3 unrestricted...

Hi, I'm in the process of revision for upcoming exams, one likely question will give a number of decays (~5) and ask if they are possible. I understand baryon number, lepton number (and parity, isospin, and strangeness) must be conserved, but for example for the following: K+ -> neutral...

What would be the best method for heating copper tubing via nichrome wire? Voltage is 10

Hello everyone . I need to ask if I want to get the right units for each parameter to be able to get the right results Can anyone define them properly? Like the gamma the initial power of pump or signal dispersion and non linear factors Thank you

Homework Statement consider y'' + 2y' - 3y = 1 + xe^x, find the particular solution The Attempt at a Solution so f(x) = 1 + xe^x f'(x) =e^x + xe^x f''(x) = 2e^x + xe^x so it looks like my particular solution is going to have a constant term, an e^x term and an xe^x term, so I can...