Numerical Definition and 775 Threads

Hello everyone and greetings from my internship! It's weekend and I'm struggling with my numerical solution of a 1+1 wave equation. Now, since I'm eventually going to simulate a black hole ( :D ) I need a one-side open grid - using advection equation as my boundary condition on the end of my...

Homework Statement Define an array with 100 integer values, and fill the array with random numbers in the range from 0-99. Then write a function named split () that reads the array and places numbers from 0-50 and another array that places numbers from 50 to 99. I wrote this code which...

[b]1. use linear interpolation to find the root of the following equations, correct to 3 decimal places, [e][/x]=3x + 1 [b]2.how to find its roots? The Attempt at a Solution

Hi there! I have to numerically solve the Schroedinger equation for a particle in a static magnetic field. Until now I've used the split operator technique using the Fourier transform. The problem is that this technique requires that the hamiltonian operator can be decoupled as: H(\vec x, \vec...

Homework Statement A boy throws a ball with v velocity upwards as well as downwards . What will be the displacement covered by the two balls if air friction and external force or viscosity is neglected ? Homework Equations According to me the equations of motions are relevant here ...

Hello, found this forum very instructive! I had this doubt of numerical integration in MATLAB. I have to perform this integration in matlab: r = 0:0.01:22.5; //necessary because they automatically become lower and upper limits of integration! theta=0:pi/100:pi; // limits are not to be...

i'm measuring a waveform (pulse) that i want to integrate the area under. i take a bunch of samples and use one of the basic numeric integration methods (Trapezoidal, Simpson's, Boole's) what is a fairly easy method to estimate the uncertainty/error of the numeric integration compared to...

An equation of the form: \frac{\partial A}{\partial t}+\frac{\partial B}{\partial x}=C I am thinking Lax-Wendroff.

Homework Statement Kindly look at the attachment for the statement. Homework Equations L^2 (psi) = E (psi) The Attempt at a Solution For Part B, I wrote Lx, Ly, Lz in operator form. Thus I get L^2. L^2 (psi) = E (psi) psi = E^-alpha.r^2/2 So I get energy eigenvalue 2 h cross...

Is there any numerical work on Green's functions in real-space and real-time? The reason I ask is that it seem the self-energy diagrams correspond to much simpler expressions in space-time than in energy-momentum. However, I suspect the space-time greens functions are sort of pathological...

I'm solving the 2D harmonic oscillator, numerically. -\frac{1}{2}\left( u_{xx} + u_{yy}\right) + \frac{1}{2}(x^2+y^2)u = Eu The solutions my solver spits out for say, the |01> state, are linear combinations of the form |u\rangle = \alpha_1 |01\rangle + \alpha_2 |10\rangle which is...

For the solution to this problem, I have reduced the number of equations down from 17 to 6. Due to algebra reasons, these equations cannot really be solved symbolically (MAPLE tried, and return four full pages packed with symbols, just for one equation). These three equations need to be solved...

Homework Statement a ball is throwm horizontally from top of a cliff with velocity 10meter per second. height of cliff above the ground is 45 meters. calculate the direction of ball to horizontal surface just before it hits the grouND The Attempt at a Solution i found time=3s...and horizontal...

Hi! I have a differential equation coming from Boltzmann transport equation which is a bit complicated and should be solved numerically instead of analytically. I managed to get a plot using Runge-Kutta with software Derive. The equation is in the second attachment. In the papers of my...

Homework Statement "The goal of this task is to check that you understood the derivation of Newton’s method in the lecture. 1. Consider a smooth function G defined from \mathbb{R}^N to \mathbb{R}^N. Suppose it admits a fixed point r \in \mathbb{R}^N. Write down the Taylor development of this...

So, I'm writing a program in matlab. I have a function of six variables, say f(x1,x2,x3,x4,x5,x6). I want to integrate over x4, x5, and x6 numerically. f is defined over a 10 sided 6-cube of points. I also want to integrate over the whole cube. So I want, F(x_1, x_2, x_3) = \int\int\int...

hi, I'm wondering how to find the approximate solution of dy/dx= e^x y y(0)=1 at x = 0.1 using the Taylor Series method. The expansion should include the first four non-zero terms. Work to six decimal places accuracy. Here is what I did but I am unsure which one is correct : first...

Say we have some partial differential equation for u(x,t) and we devise a numerical method to solve it. For example if we say unm is the solution at x=hm and t=kn with m=0,...,M and n=0,...,N where h and k are the step-lengths, and then our method is something like...

Mechanics Kinematic General Concept question, not a numerical!? I'm really confused concerning the positive direction and the acceleration taken while concerning the motion of the ball! Well, the main thing that i wanted to ask is that if 2 balls are been projected at the same time in two...

Hi, I'm searching for days for a numerical integration methode for discrete data given at non-equidistant nodes. The simple Simpson rule can only be used for equidistant nodes so I'm looking for methode which I can solve my problem. Any suggestion is welcome! Thanks in advance!

I have a function with one and only one local/global maxium... (i.e. half the function has positive slope, half the function has negative slope). And I want to find the maximum point on the function. How can I find the function's max? I was thinking of turning the function into its...

y' = 3 + t - y, y(0) = 1 A) Find the approximate values of the solution of the given initial value problem at t = 0.1, 0.2, 0.3, 0.4 using the Euler method with h = 0.1. B) Repeat part A with h = 0.05. Compare the results found in A. I did part A correctly, but cannot get the right...

Hi, I recently need to do some numerical simulation by Euler method to solve a PDE. However, I noticed that there are some errors which are obtained with bigger numerical steps, when applying Euler scheme. Since my major is not mathematics, I do not know what this phenomenon is called. I...

Homework Statement Differential equations are important in physics.Consider Solving the differential equation dy/dx = Σ(from i to N) (ai) (x^i) Using Euler ,Midpoint ,4th order Runge -Kutta methods.For each of these methods what is the largest value of N that would lead to an exact solution ...

Hi Everyone, Apologies if this is posted in the wrong place. I am trying to produce numerical solutions for the following initial value partial differential equations, namely the overdamped Schmoluchowski equation \frac{\partial p(x,t)}{\partial t}=-\frac{\partial}{\partial...

Hi, I need help with the following numerical analysis questions. The textbook I'm using (Intro to Numerical Analysis by Stoer) doesn't have many examples so I'm having a lot of trouble figuring out what exactly I should be doing. "Evaluating the summation as i goes from 1 to n of a sub i in...

Homework Statement Find the order of error of this numerical method: f''(x_i+\frac{h}{2})\simeq \frac{\Delta ^2f_i}{h^2} Homework Equations Taylor's theorem, Newton's interpolation polynomial and its error. The Attempt at a Solution I started from Taylor's expansion at x_i and...

Hi! My problem is connected with solving 3-dimentional Schrodinger equation for descrete spectrum. I need to consider arbitrary 3D-potential and find characteristics of boundary levels, produced by this potential (energy levels, quantum numbers...) All I found over the internet were...

The amount of a uniform distributed radioactive contaminant contained in a closed reactor is measured by its concentration (c) (Becquerel/liter or Bq/L). The contaminant decreases at a decay rate proportional to its concentration; that is Decay rate(dc/dt)= -kc Where (dc/dt) is the change in...

MATLAB - "for" loop for numerical integration Hi. The following bit of MATLAB function is supposed indefinitely integrate successive points: % Explode triplet format into vectors x_in = data_in(:,1)'; y_in = data_in(:,2)'; e_in = data_in(:,3)'; x_left=x_in(1:end-1)...

Hi there, I was expecting to find a "simulations forums" somewhere here, if there is a better place for this thread please let me know :) OK, here's the problem: I'm trying to make a simulation with PYthon, at first with a square potential, for simpler potential/boundary conditions. But...

write program calculate http://<a [/URL] href="http://www.codecogs.com/eqnedit.php?latex=f^{"}\left ( x \right )" target="_blank"><img src="http://latex.codecogs.com/gif.latex?f^{"}\left ( x \right )" title="f^{"}\left ( x \right )" /></a> x=0 http://<a [/URL]...

Hi there, I am working on a problem in Fluid dynamics. I've written a code in MATLAB which finds the shape of the free surface of the liquid based on Newton Relaxation. The code is fairly robust and produces good results which agree with current papers on the same problem. Unfortunately...

Homework Statement I need to understand why \left|4+i \right|=4.123 and why this is shown by: \sqrt{4^{2}+1^{2}}=4.123 Homework Equations i^{2}=-1 The Attempt at a Solution If I find the square root of this expression squared, then I come up with \sqrt{16-1+8i} which is...

My dear all! Hello! How are you all? Let us assume that we have given an equation of a curve like y=3x2+3x-1 By numerical analysis(bisection method) I want to find its root. Everything is fine in the case if interval is given (a,b). But my problem is that if interval is not given then...

http://arxiv.org/abs/1012.3081 The Universal RG Machine Dario Benedetti, Kai Groh, Pedro F. Machado, Frank Saueressig 38 pages (Submitted on 14 Dec 2010) "Functional Renormalization Group Equations constitute a powerful tool to encode the perturbative and non-perturbative properties of a...

Homework Statement Consider the implicit (not actually sure wether that's the correct english word, my material is in Finnish and I'm Swedish-speaking :smile:) method xj+1=xj+h/2(f(tj,xj)+f(tj+h,xj+1)) a)Write an appropriate Runge-Kutta scheme b) What is the methods rank when we use the...

Homework Statement I want to approximate the following integral: \int^{1}_{0}\frac{1}{x}dx using the trapezoidal quadrature rule. However there is a singularity at x=0. Homework Equations trapezoidal method: \int^{a}_{b}f(x) dx \approx...

I'm searching a book, or a place on the net where I'll find tons of examples of numerical problems in physics (mainly quantum mechanics) written in Python. I have tons of books about Python, but none have good examples on problems like tunneling, solving Schrodinger eq for various potentials...

In Newton's Rings Experiment, what will be the order of the dark ring which will have double the diameter of that of the 20th dark ring? Wavelength(lambda = 5890 Angstrom); Radius of curvature is not given. Thin film is made of air, so refractive index is 1. And the light is incident normally...

Hello everyone, Does anyone know how I can compute the jacobian matrix numerically in matlab? So, I have the following. A 100x100 image and at each pixel, I have a 2 element gradient vector. What I would like to do is compute the jacobian matrix (wrt to the spatial location), at each pixel...

Please anyone help me with stability proof this next numerical method \dfrac{u^{n+1} - u^{n}}{\vartriangle t} = (u^{n+1}u^n)I am trying make : \begin{equation*} \begin{split} u_2^{n+1} - u_1^{n+1} & = \displaystyle\frac{u_2^{n}}{1-\vartriangle tu_2^{n}} -...

Homework Statement Determine constants c and C that do not depend on vector x. For this to be true: Use this result and the definition of matrix norms to determine constants k and K so that: Homework Equations The Attempt at a Solution I've done half of this...

Homework Statement y=(a*exp^b*x)/(c+d*exp^m*x) The Attempt at a Solution (1/y)=(c+d*exp^m*x)/(a*exp^b*x) y(new)=1/y y(new)=(c/(a*exp^b*x))+(d*exp^m*x)/(a*exp^b*x) i stopped here and i don't know how can i complete?

First off, I know I can use the trapz or quad functions on matlab, but I want to derive my own numerical integration code. The problem is more complicated than this, but basically I need to be able to numerically integrate in MATLAB to continue with the homework assignment. If y = x^2 is...

First off, I know I can use the trapz or quad functions on matlab, but I want to derive my own numerical integration code. The problem is more complicated than this, but basically I need to be able to numerically integrate in MATLAB to continue with the homework assignment. If y = x^2 is the...

Homework Statement I want to derive equation Eq. 9.4.6 in Numerical Recipes from the expressions given, as stated in the book! The equation represents the next (i+1 th) deviation \epsilon from the true root. Eq. 9.4.6: \epsilon_{i+1} = -\epsilon_i^2 \frac{f''(x)}{2f'(x)} Homework...

Hello, I have a problem with numerical solution of the system of ODE's (geodesic eqs.) in Mathematica. The only relevant command I have found is NDSolve. It works perfectly, unless my equations contain functions which are again computed using numerical methods. Simple example illustrating...

Not sure if this is the right place. Mathematica has a function BesselK[0,x] that returns the value of the modified Bessel function K_0 at x. Is there public documentation of how this algorithm works? If not, is there documentation regarding any algorithm of K_0? I am hoping it doesn't...

Sorry for the wordiness of the thread title. Basically I'm wondering, if you have two implicit functions, F(x,y)=0 and G(x,y)=0 (typically rational functions with numerator and denominator very high degree polynomials), both dependent upon the same K (in my case > 34) dimensional set of...