Numerical Definition and 701 Threads

1. In a 3 x 3 square, place the numbers 2,2,2,3,3,3,4,4,4 in it so that when any line of three numbers is added up in any direction (including diagonally) the total is always 9. 2. I have tried for hours, can anyone tell me if this problem is actually possible? The best I get is when I do 234...

Oops, I was to quick here. At least, there is no instability. Nevertheless I would write ##\mathrm{Corr}(R)=0.12(1+\exp(-50 \mathrm{PD}))## instead of Correlation (R) = 0.12 × (1 – EXP (-50 × PD)) / (1 – EXP (-50)) + 0.24 × [1 - (1 - EXP(-50 × PD))/(1 - EXP(-50))]

how do i numerically calculate a double integral? as i understand simpsons 3/8 rule is the optimal method for a single integral, is it still true for double integrals? if so, how do i extend the 3/8s rule to do a double integral?

Hello, can someone advise me how to solve numerically ODE which consist of function with "critical point" (Im not sure if it is good definition)? I mean for example this one: y'(x)=\frac{\sin{x}}{x}, where in x=0 has function a "problem". I know that limit ->1 but in numerical solutions it...

Hi, I am trying to plot a function subjected to a nonlinear wave equation. One of the method I found for solving the nonlinear schrodinger equation is the split step Fourier method. However I noticed that this method only works for a specific form of PDE where the equation has an analytic...

Hello, I have two different discrepancies to this system: a) How and when is possible to have more solution of differential eq. or their system for same initial problem? For example this is happening in following system. It is written about this system: "Different value of constant \dot{M}=4\pi...

Homework Statement A ball was dropped through a known vertical distance with the time of drop also recorded. The aim of the task is to create a numerical model in excel in order to approximate the drag coefficient. Homework Equations This is my method. 1. FBD for the ball falling. (assume...

The problem statement Based on an analytical solution for the concentration profile of a dissolving sphere, I am supposed to use a numerical method to find the time at which the sphere has fully dissolved. This is not so much a question about specific values - but about the technique by which I...

I can't compute the integral: \int \frac{\arccos(\sqrt{x^2+y^2})}{\sqrt{x^2+y^2}}\frac{x-a}/{(\sqrt{(x-1)^2+y^2})^3 dxdy on an unit circle: r < 1. for const: a = 0.01, 0.02, ect. up to 1 or 2. I used a polar coordinates, but the values jump dramatically in some places (around the 'a' values)...

Hi, I'm not a bright programmer , but I have to solve the fallowing equations: ##\frac{df}{dt} = \alpha f -\beta f + \theta g - (f+h)f## ##\frac{dg}{dt} = \psi f- \phi g## ##\frac{dh}{dt} = \xi f+ \mu h -\tau h + \epsilon w- (f+h)h## ##\frac{dw}{dt} = \nu h - \chi h## Where ##f(t)## ...

Hi, I have two numerical matrices, A is 150*1 matrix (A=rand(150,1)) and B is a 1*5 matrix (B=rand(1,7)), and I need to have the jacobian of A with respect to B, that should be a 150*7 matrix, anyone help is appreciated. Mathias

I am would like to solve this differential equation: Where http://ieeexplore.ieee.org.ezproxy.uniandes.edu.co:8080/ielx5/8/6493417/6409989/html/img/6409989-eqdisp-3-small.png Could you give me some practical ideas about the required software and methodology? Thank you very much

Dear All, Can someone suggest me an appropriate routine (in Fortran) or command (in mathematica) to perform numerical integration of a function, which is specified numerically on a one dimensional grid with equal spacing (and we cannot generate additional data on other grid points)? There are...

Let f(x^2) be a polynomial. I would like to carry out the integration \int_a^b f(x^2) dx using quadrature rule. Suppose a and b > 0 and are arbitrary and the degree of f(x^2) is 2N. I would like to know if there is a possibility to reduce the sampling points down to N/2?

The Diode in the circuit shown below has the non linear terminal characteristics as shown in the figure.Let the voltage be "coswt" V . Question 3.1.33 and my attempt is shown in the figure.

Edit:whoops wrong forum mods please move 2nd edit: I just had dinner then got back on the computer, input some points and saw a beautiful elipse.(complete with a fascinating flower petal design due to inaccuracies) Weird lol! No idea why it wasnt working before Now to implement RK4 bwahahaha...

Hello Forum, The numerical aperture NA of a lens is usually a parameter (adimensional) that indicates the lens ability to collect light. The concept of NA is usually introduced in fiber optics where we are concern with launching light into the fiber. But NA is also discussed in microscopy...

Homework Statement This question being for my physics summer work states "List three properties that all numerical answers must have to be correct" Homework Equations None The Attempt at a Solution 1. must be a numerical value? 2. must show accuracy. 3. must show precision.

In the late 1980's I asked my logic professor if there was some kind of logical and/or mathematical process which unified numerically based mathematics with true-false based symbolic logic.He told me that someone had written a lengthy book which apparently proved that it was totally impossible...

Hi! I posted a new thread about a week ago, but so far no one was able to help me: https://www.physicsforums.com/showthread.php?t=761892 I wasn't sure if I posted in the right forum, so I'm posting it here hoping to reach a wider audience :) Any help is greatly appreciated! -Tusike

Hi! I'm trying to compute air flow between chambers for a project. I'm having a numerical oscillation problem, and I've created an example Simulink program that highlights the cause. Please see the attached Simulink model for a clear understanding; in the following I will do my best to give...

Homework Statement Here I am, trying to get the trajectory $(x(t),y(t))$ that will minimize the following Lagrangian (i.e. the integrand of the functional) between $(-1,-1)$ and $(-1,y_{eff})$ where $x_{eff}$ is defined as the point where $V(x_{eff},-1)=V(-1,-1),x<0$. So here's the...

Hi, Are there any numerical techniques I can use to solve differential equations with periodic boundary conditions? I know of several techniques for other kinds of boundary conditions (such as Runge-Kutta method, Euler method etc.), but I am interested in knowing how to numerially solve...

Hi, When we want to solve the Navier-Stokes equations coupled with the conservation of mass for incompressible fluids using the primitive-variable approach, we have to face to the problem that the equation for the continuity equation does not contain the pressure which leads to spurious...

I need to compute numericaly n-body sys. interacting acording to the Weber force: http://en.wikipedia.org/wiki/Weber_electrodynamics and I have a problem with the acceleration on rhs: r'', because the acceleration is unknown, due to the Newton law: F = ma, and we need just 'a' to do next...

I am trying to find the density, scale radius and normal radius of the milky way's halo. But these things are pretty hard to find. I want to find them so I can input them into the NFW profile:

I had tried to solve but the problem is here initial guess is given as 1 and 1000 but both has positive value of function , so wat to do now how to determine x3 which is x1+x2, wat to take x1 and x2 in second iteration, just guide me how to solve Thanks a lot for ur replies

Hi, I need to calculate area of an irregular polygon which can be of any complex shape numerically i.e. using numerical integration techniques. Please can anyone suggest any reference material / best way of going about this efficiently? Akash

Homework Statement Show that for a set A\subsetN, which is numerically equivalent to N=Z+, and the set B = A \cup{0}, it holds that A and B are numerically equivalent, i.e., that A \approxB Hint: Recall the definition of A≈B and use the fact that A is numerically equivalent to N. Note...

Numerical integration methods applicable to a type of definite integrl Hey, so I've been working on a program to numerically integrate an integral of the form ∫xnf(x) dx, LIM(0 to INF.) Here n can go to negative non integral values, say -3.7 etc. and f(x) is a function of sin, cos and...

Two criteria 1. Freely Available 2. Large support for additional scientific libraries/packages/modules for reuse http://en.wikipedia.org/wiki/Comparison_of_numerical_analysis_software Which one would you recommend and why?

Hi, I want to solve one dimensional Schrodinger equation for a scattering problem. The potential function is 1/ ( 1+exp(-x) ). So at -∞ it goes to 0 and at ∞ it's 1. The energy level is more than 1. I used Numerov's method and integrated it from +∞ (far enough) backwards with an initial value...

The nonlinear oscillator y'' + f(y)=0 is equivalent to the Simple harmonic motion: y'= -z , z'= f(y) the modified Symplectic Euler equation are y'=-z+\frac {1}{2} hf(y) y'=f(y)+\frac {1}{2} hf_y z and deduce that the coresponding approximate solution lie on the family of curves...

Show that the explicit Runge-Kutta scheme \begin{equation} \frac {y_{n+1} -y_{n}}{h}= \frac{1}{2} [f(t,y_{n} + f(t+h, y_{n}+hk_{1})] \end{equation} where $k_{1} = f(t,y_{n})$ applied to the equation $y'= y(1-y)$ has two spurious fixed points if $h>2$. Briefy describe how you would...

I have a system of linear differential equations with known boundary conditions. First of all what is the general solution to such a system? I know it is exponentials with the eigenvalues, but I couldn't find any place where the exact full solution was stated. Second of all, I want to write a...

Hello everyone, this is my first thread in this comunity. I explain my problem: I have a triangle mesh http://en.wikipedia.org/wiki/Triangle_mesh where at every vertex coincide a mass element and on every edge I add a spring. I would like simulate a deformation model. My idea derive...

I have thousands of triple integrals with very ugly integrands to run. Each of those computations takes about an hour in R on a mediocre machine. For uninteresting reasons, when I was initially coding this up, that's the language and machine I had to work with. But now my options are wide...

This is from Peter Smith's Gödel without tears. I don't agree with this. If it appears in the list of p.r. functions then it is p.r. I don't see why he thinks that if x is in the list of p.r. functions then it is not p.r.

Homework Statement Solve the inhomogenous partial differential equation \frac{∂^{2}u}{∂t^{2}}-\frac{∂^{2}u}{∂x^{2}}=-6u^{5}+(8+4ε)u^3-(2+4ε)u by using the NDSolve function in Mathematica for the interval [0,10] x [-5,5]. Homework Equations Initial conditions: u(0,x)= tanh(x)...

Hello all, Suppose I have a simple 1-D signal and I want to compute the hessian. In that case, it should generalise for second derivative for normal scalar functions. So, I observe the signal as v = [x_1, x_2, x_3, x_4...]. Then, numerically the hessian is given as (assuming I am only...

Homework Statement Use a Taylor Polynomial about pi/4 to approximate cos(42){degrees} to an accuracy of 10^-6. *To get an accuracy of 10^-6, use the error term to determine an nth Taylor Polynomial to use. Homework Equations x = 45 or pi/4, x0 = 42 or 7pi/30 cos(x) = Pn(x) + Rn(x)...

Hi, I have to use a wide 5 point stencil to solve a problem to fourth order accuracy. In particular, the one I'm using is: u'' = -f(x + 2h) + 16f(x + h) - 30f(x) + 16f(x - h) - f(x - 2h) / 12h2 or when discretized u'' = -Uj-2 + 16Uj-1 -30Uj + 16Uj+1 -Uj+2 / 12h2 In addition to...

Okay, I'm in a bit of a pickle here. Got the exam on thursday and (surprise) I am utterly clueless. I cannot grasp a lot of concepts, but here's some I'd like to at least get an idea of: Factorization method. I only scrapped that it is a special case of Gauss' Exclusion method, that you take a...

Can anyone explain to me why the gaussian white noise term is multiplied by the square root of the time differential when we turn the Langevin differential equation into a finite difference equation for the purposes of integration? http://pre.aps.org/pdf/PRE/v50/i6/p4404_1 The step I...

Homework Statement Hi, I have to do a simulation of two non linear dynamical equations which represent a electromechanical system. (An inverted pendulum attached to a cart moving over a rail). I am going to simulate the response via numerical methods programmed in LV. (I am trying firts with a...

Hi guys, I need to simulate wave propagation for a nonlinear dispersive wave PDE and since I can't find proper resources for handling nonlinear PDEs numerically, I would appreciate any help and clues. the PDE is in the form of utt-(au+bu2+cu3+duxx)xx=0 Romik Ps: BC: Clamped at both ends IC...

Hi, I have a question about resolution as defined by rayleigh's equation r = 0.61 x lambda/numerical aperture The maximum half angle of acceptance of a lens is 90 degrees and the sine of this is 1. At this point the only thing that can increase the value of the denominator in the equation...

I am currently doing my bachelors in Mechanical engineering engineering and planning to pursue physics after completion. I have to choose an elective the coming semester. One of the electives offered is 'Numerical Methods for Engineers' and the modules covered include Error in numerical...

I would like to find a FORTRAN subroutine or a good way to minimize function numerically.So basically my function has 20 variables and I am able to provide analytic form of the first and the second derivative of the function. Basically what I want is: have the form of the function of 20...

Sorry, but this is the only subject I could not pass even if I gave it my all every day and night of the semester. And I will still surely fail this subject, but as a last resort I will try to post my problem here, hoping to get solution and maybe an explanation. Sorry if some of the phrasing...