Method Definition and 1000 Threads

Hello, I am wondering what the purpose of the Ponchon Savarit method is for determining the theoretical number of stages using an enthalpy-concentration diagram. From what I am seeing, the method requires using a xy diagram with the equilibrium curve. Isn't it superfluous to use the H-x diagram...

Hi, I have been trying to find an integral ## \int_{-\infty}^{+\infty} \frac{ e^{-\sqrt{(x^2 + 1)}}}{(x^2 + 1)^2} dx ##. I initially posted this question in the complex analysis forum since I felt it might be done using contour integration. However now I realize it might not be the best way...

Hello, This is my first post here. So I hope I'm posting in the right place, sorry if not. http://homes.soic.indiana.edu/classes/spring2012/csci/b553-hauserk/Newtons_method.pdf I am trying to solve the following numerical optimization function using Netwon's Method: So, if I have the gradient...

Hello, I'm trying to understand the application of Green's function to find the potential better. I apologize in advance if I start mixing things up a little. From what I understood and seen, we use this method (Green and method of images) in known symmetries (cylindrical/spherical/planar) and...

Hi, I'm not sure if this should actually be in the "homework" section instead. I'm posting it here because it's more of a pedagogy question, I think, but I could be wrong about that also. Ok, I tutor calculus, and when I do u-substitution, I always solve for something (not always dx), so that...

Homework Statement Obtain the voltage Vx in the network of Fig.Q11, using the mesh current method. (Ans: Vx=4.35∠-194.5) Homework EquationsThe Attempt at a Solution I am not getting the correct answer, are my loop equations correct ? 10 - 2*i1 + 2j*i1 -5j(i1+i2) -5(i1+i3) = 0 4.33 + 2.5j -...

Hello, can anyone give me the general instructions of solving shooting method problem: dy1/dx=-y1^2*y2 dy2/dx=y1*y2^2 with the boundary conditions: y1(0)=1, y2(1)=2

Hey, I was hoping someone could clear this up for me. When using this method, how do you get the final equation of motion, that's where I am confused. So I know I start off using Lagrangian (T - U) -> momentum (partial L/ partial q dot) -> Hamiltonian T+U, and then using the hamiltonian...

Homework Statement Prelim: my question is about a very specific part of a question whereby the student is asked to derive the final formula for the general solution in two vars, but I will post the entire question for clarify. Newton's Method for approximating the roots of an equation f(x)=0...

Note that the general solution to $y'' - y = 0$ is $y_h = C_1e^t + C_2e^{-t}$ In the following, use the Method of Undetermined Coefficients to find a particular solution. a)$y'' - y = t^2$ So here is what I have so far $y_p = At^2 + Bt + C$ $(y_p)'' = 2A$ Ive got $A = -1, B = 0 , C = 0$ so...

Homework Statement I am given the wave eqtn: (\frac {d^2} {dr^2}+\frac{1} {r} \frac {d} {dr})\Phi(r)=−k^2\Phi(r) The problems asks to 'show that the substitution $$ \Phi=r^{-\frac{1} {2}} \phi $$ gives an eqtn for which the Numerov algorithm is suitable'. Homework EquationsThe Attempt at a...

Thanks for reading. I am given the wave eqtn $ {[(\d{}{r}})^{2} +\frac{1}{r}\d{}{r}]\Phi\left(r\right)=-{k}^{2}\Phi $ The problems asks to 'show that the substitution $ \Phi={r}^{-\frac{1}{2}}\phi $ gives an eqtn for which the Numerov algorithm is suitable'. I get $...

Hi, I'm reading Ogata's Modern Control Engineering, and when he talks about the representation of a differential equation in state space he divides the method in two. The first one is when the input of the differential equation involves no derivative term, for example: x'(t)+x(t)=u(t) The...

i want to solve a nonlinear PDE with finite difference method ,but using just discretization like in linear PDE , it will lead to nowhere , what's the right way to use FDM to solve nonlinear PDE or could someone provide me with book's titles or articles that can help me solving a nonlinear pdf...

Homework Statement My question is quite specific, but I will include the entire question as laid out in the text Consider the problem of minimizing the function f(x,y) = x on the curve y^2 + x^4 -x^3 = 0 (a piriform). (a) Try using Lagrange Multipliers to solve the problem (b) Show that the...

Hello! (Smile) Consider the initial value problem $$\left\{\begin{matrix} y'(t)=f(t,y(t)) &, a \leq t \leq b \\ y(a)=y_0& \end{matrix}\right. (1)$$ I want to write a program that implements the following numerical method to solve $(1)$ $\left\{\begin{matrix} y^{n+1}=y^n+h[\rho...

If we study model fit on a nonlinear regression model $Y_i=f(z_i,\theta)+\epsilon_i$, $i=1,...,n$, and in the Gauss-Newton method, the update on the parameter $\theta$ from step $t$ to $t+1$ is to minimize the sum of squares...

Hey! :o In my notes there is the following example about the energy method. $$u_{tt}(x, t)-u_{xxtt}(x, t)-u_{xx}(x, t)=0, 0<x<1, t>0 \\ u(x, 0)=0 \\ u_t(x, 0)=0 \\ u_x(0, t)=0 \\ u_x(1, t)=0$$ $$\int_0^1(u_tu_{tt}-u_tu_{xxtt}-u_tu_{xx})dx=0 \tag 1$$ $$\int_0^1...

Given series:1,2,5,12,25... How did they get :##T_n=a(n-1)(n-2)(n-3)+b(n-1)(n-2)+c(n-1)+d## And for series like 3,7,13,21,... they have given ##T_n=an^2+bn+c## How do you get these equations?

Hello! (Wave) We consider the initial value problem $$\left\{\begin{matrix} y'=\lambda y, & t \in [0,\infty), \lambda \in \mathbb{C}, Re(\lambda)<0 \\ y(0)=1 & \end{matrix}\right.$$ Since $y^n=(1+h \lambda)^n, n \in \mathbb{N}_0$ is the sequence of approximations that the Euler method...

Homework Statement After turnig of magnetic-optic pit, cold cloud of atom 87 Rb is expanding. Size of cloud after time t, is given with relation: where, k_B is Boltzman constant, m mass of 87 Rb. Draw a plot, then use least squares method to find temperature T, and initial size of cloud...

Homework Statement *I am not sure if this should be in the computer science section or here? I am trying to graph the densities, of the Lotka-Volterra prey and predator model, as a function of time, i.e. ##p(t)## vs ##t## and ##q(t)## vs ##t##. Also, the phase space, i.e. ##p## vs ##q##, but...

Homework Statement Determine the force in member BE of the loaded truss. See the attached picture. Homework Equations Sum of the Moments = 0 Sum of the Forces = 0 The Attempt at a Solution [/B] Sum moments about A to get: -12L - 56L +40Dy = 0 Dy=1.7L Sum the forces in the y...

Hi, Apart from the Euler's method, is there any other method (with better efficiency) that can let us solve an Ordinary Differential Equation of the form \frac{dy}{dx}= f(x,y)?

Hello! (Wave) I want to solve the following problem: $$u_x(x,y)+(x+y)u_y(x,y)=0 , x+y>1 \\ u(x,1-x)=f(x), x \in \mathbb{R}$$ How could I do it? Could we apply the method of characteristics? In my lecture notes, there is an example on which this method is applied. This example is of the form...

I am confused on how to use the Runge Kutta method to solve for a relationship between the Chrandrasekhar Mass and radius on the following two equations of state: dx/dr = (-5/3)*(M/r^2)*[sqrt(1+x^2) /x] where x(r=0) = x_c dM/dr = +3*(r^2)*(x^3) where M(r=0) = 0 where M is the mass, r is...

Homework Statement How do I create an instance of a class in a method? Homework Equations None The Attempt at a Solution I am a bit rusty whenever I think of instances. I always think of main method and objects when I see instance which gets me confused on what to do with the following...

Hello! (Wave) The differential equation $y''+xy=0$ is given. Find the general solution of the differential equation (with the power series method). That's what I have tried: We are looking for a solution of the form $y(x)=\sum_{n=0}^{\infty} a_n x^n$, where the radius of convergence is...

Hi, I'm trying to program an arduino to generate a Trapezoidal Motion Profile to control a DC motor with a quadrature encoder. Essentially, the user will input the desired Target Position, Max Velocity and Acceleration (decel = -accel) and the code will calculate the target position versus...

Homework Statement http://oi59.tinypic.com/2h65cm1.jpg[/B]Homework EquationsThe Attempt at a Solution [/B] All triangles: angles A = B = 53.13 degrees, angle C = 73.74 degrees from cosine law and the 180 degree ruleBut it looks like all of the joints in the bridge have more than 2...

When using the variational method for the Helium atom, we determine that the lowest possible energy occurs when 1<z<2 where z is the atomic number. My professor elaborated that the number is within this range because there is a probability that the electron may be so close to one of the protons...

Hello! (Wave) We take into consideration the following ODE: $\left\{\begin{matrix} y'=2t &, 0 \leq t \leq 1 \\ y(0)=0 & \end{matrix}\right.$ Its solution is $y(t)=t^2$. The following graph shows geometrically how Euler's method work. $$y^{n+1}=y^n+hf(t^n,y^n)\\y^{n+1}=y^n+h \cdot 2 \cdot...

Hello! (Smile) Theorem Let $f \in C([a,b] \times \mathbb{R})$ a function that satisfies the Lipschitz condition and let $y \in C^2[a,b]$ the solution of the ODE $\left\{\begin{matrix} y'=f(t,y(t)) &, a \leq t \leq b \\ y(a)=y_0 & \end{matrix}\right.$. If $y^0, y^1, \dots, y^N$ are the...

Hello! (Smile) Theorem: Let $f \in C([a,b] \times \mathbb{R})$ function that satifies the total Lipschitz condition and let $y \in C^2([a,b])$ the solution of the ODE $\left\{\begin{matrix} y=f(t,y(t)) &, a \leq t \leq b \\ y(a)=y_0 & \end{matrix}\right.$ If $y^0, y^1, \dots, y^N$ are the...

Homework Statement This is a diagram from "Structural Analysis" by Aslam Kassimalli while solving frames using slope-deflection method. In the figure, the tangent to the deflected shape at C` is parallel to the original member AC implying that the slope at C is zero. However, later they have...

Hi everybody, The situation is the classic one: a point charge q+ in a distance d above a conductor plane grounded: The conductor is grounded so V = 0, for z = 0. Also, far away from the system (x2 + y2 + z2 >> d) V --> 0 The argument to replace it for a q- charge seems perfect to me. What I...

Homework Statement Suppose I have a subclass called, Cashier, and a super class named, Clerk. How do I make a method that is called on a Cashier object and takes in an instance of Cashier? What method has a structure like this? Homework Equations NoneThe Attempt at a Solution This method is...

-simple procedure designed to absolutely synchronize clocks- Picture the face of a very large clock with a one hand. Let's place a small clock A at the 9 o'clk position of the large clock, and let's place another small clock B at the 3 o'clk position. We use clock A to time the large clock's...

Just a question How does solving the nonlinear schrodinger equation using split step Fourier method makes us understand the four wave mixing process in optical fiber ? Any examples on how that happens Thank you

Hi all! I need to decide on the production philosophy of an SEV(small electric vehicle) as a final part of my thesis project. Up until now, I have designed the package layout and body and performed a FE analysis (topology optimization) to arrive at a reasonable body-in-white structure. I did a...

Hi there, I am preparing to use the scotch tape method to get hex-Boron Nitride thin film from hBN powder. As far as I know, the available particle size for hBN is 10 um at most, is it possible for me to get hBN thin film using the peel off method with size larger than 10 um? If so, what is the...

For fun, I thought I would try to derive the moment of inertia of a square using different approaches (in each case, changing the differential area being integrated). Everything went well until I tried the approach of first considering the disk in the center of the square, then adding the bits...

Greetings. I was wondering if anyone knew of a way to calculate the efficiency of Newton's Method for a given function: I have an equation f(x) and I'm trying to find a value of x = x0 such that f(x0) = 0. So I start with a guess x0 and then use that to find a second (usually closer) guess...

Homework Statement Solve the BVP for a vibrating string with Separation of Variables/Fourier's method. \frac{\partial ^2}{\partial ^2 t} u(x,t) = c^2 \frac{\partial ^2}{\partial ^2 x} u(x,t) The string is of length L with each end fixed, ie u(0,t) = u(L,t) = 0 The Attempt at a Solution I...

Up to this point I have got a grasp of some basics of "steepest descent method" to evaluate the integral of a complex exponential function ##f(z) = \exp(A(x,y))\exp(iB(x,y))##. Using this method the original integration path is modified in such a way that it passes through its saddle points...

Hi, I want to understand how stress concentration factor or notch factor is considered in FEA method. Lets assume a case of stepped shaft which has got the left end of the shaft fixed with rigid wall and the other end being pulled by an axial load. In the case of conventional calculation...

Can someone check this is correct? Using the Newton Raphson method with X0=2 to find the root of the equation: x^3-x-1=0 (correct to 4.d.p) My answer is: f'(x)= 3x^2-1 xn+1= 2-x^3-x-1/3x^2-1 xn+1= 2-2^3-2-1/3(2^2)-1 x1= 17/11 x2= 17/11-(17/11^3)-17/11-1/3x(17/11^2)-1 = 1.3596

I am working on a take home with a group of students and we all got different answers for this problem... can anyone look over it and tell me where I am going wrong?? Let me know if any of my work is confusing...

I am not understanding how to use the method of steepest descent aka the saddle point method. Any help would be appreciated, especially step-by-step explanation!

Hi all, I have a quick question. I was taught this, but wasn't explained to at all why it is the case. So let's say I have a differential equation with constant coefficients i.e. y'' - 4y' + 4y = e^2x And the general solution to its associated homogeneous equation is Ae^2x + Bxe^2x [A &...