Numerical Definition and 701 Threads

1. Define numerical equivalence of sets 2. I'm not sure how in depth the definition needs to be, how is my current def? 3. X is numerically equivalent to Y if \existsF:X\rightarrowY that is bijective or there are two injective functions f:X\rightarrowY and g:Y\rightarrowX

Hi, I have an excel spreadsheet that calculates the pressure inside a piston chamber, that is a function of time. I want to calculate the distance the piston moves, this is my situation. P=F/A, therefore force on piston = PA F = M(piston).a so ma = PA, a = P(t)A/m its all numerical in...

I am supposed to write a program to decompose matrix A with PLU-decomposition. I have this text and I am trying to understand some parts of it. The text with % in front of it is in Icelandic and doesn´t matter. function [P,L,U,r] = PUL_thattun(X) n=length(X); L = zeros(n,n); U = X...

Hi all, this (probably easy) problem from numerical analysis is giving me trouble. I can't seem to get started and need some poking in the right direction. Homework Statement Consider the following claim: if two floating point numbers x and y with the same sign differ by a factor of at...

ive been given this question for a uni assignment: given the function: f (x) = 5(x^1.3) +1.5(7x − 3)+ 3(e^− x) + ln(2.5(x^3)) find the first derivative at all possible points within the interval [0, 6], with step length h = 1 for: forward difference aproximation, backward difference...

I have some data in a text file. I want to import this data into Mathematica, and then I want to calculate the numerical derivatives of this data. In particular, I need to find the y value where the first derivative is equal to zero. I can import data. I can use the ND function for numerical...

I'm just a neuroscientist, so forgive me if the answer to this question is either obvious, or the answer is that it is impossible, obviously. Basically, this image should outline the question clearly http://img713.imageshack.us/img713/2569/mathsissuefixedyxs.gif (And Y0 is always 1)Also, I...

Homework Statement Merry Xmas~ I hope there's still someone online during the holiday season. I'm trying to solve a set of static laser rate equations but with log in the expression. I think, there's no analytic solution but I don't really know how solve the problem numerically with Matlab...

Homework Statement I was asked to model the blast-wave of an explosion using Sedov's solution in MATLAB, but I'm not really sure where to begin. Most of the programming I have done has been x=linspace(1,1000,1000); for i=1:1000 y(i)=x(i)^2; end type of code, and this one...

Homework Statement [U][t]=-U+k[U][xx] u(x,0)=U(L,0)=0 u(x,0)sin(pix/L) Write down difference equations for the approximate solution of this problem using the following methods: 1)forward difference 2)backward difference 3)crank nicholson Homework Equations I can do...

Hi there I'm in desperate need for your help! I need to solve the rocket motion equation numerically in Maple or some other program. I'm having trouble writing the ODs in the program. I have derived the rocket motion equation in a single dimension: \frac {d\vec v_r(t)}{dt} = - \...

is there one that is stable and accurate?

Hey, I am a physics undergrad, and I have been recently given a task to help my physics instructor with providing visual aids and numeric examples for his class. Meaning for a given number of problems in the textbook I will take the analytic solutions and make a numerical example(s) out of it...

i am now reading a prl paper the authors used numerical simulations to study a nonlinear system in some parameters, the authors state that system enters into chaos My numerical simulations are the same as that of the authors in the regular regime but in the chaos regime, my...

Background: For an oscillating wing that will be used in a tidal generator I am trying to model the position (as function of time) of an underwater airfoil whose movement is limited to vertical motion. The free body diagram is very simple. When the airfoil is positioned for upward travel, the...

i am now reading a prl paper the authors used numerical simulations to study a nonlinear system in some parameters, the authors state that system enters into chaos My numerical simulations are the same as that of the authors but in the chaos regime, my simulations are quite different...

The following code is just an example. I try to apply mnbrak.f90 to my function f=(x-i)^2. I want to make i globle variable. If I use internal procedure, I can not use mnbrak.f90, since it can not accept the internal procedure. How do I deal with it? Thanks! PROGRAM xbrent USE nr USE...

u := x (4 - y - x^2) v := y (-1 + x) (-2,0) du := (4 - y - 3 x^2) dx - x dy dv := y dx + (-1 + x) dy x := -2 + Cos[\[Theta]] y := 0 + Sin[\[Theta]] dx := -Sin[\[Theta]] dy := Cos[\[Theta]] Integrate[1/(2 \[Pi]) Expand[(u dv - v du)/(u^2 + v^2)], {\[Theta], 0, 2 \[Pi]}] If...

Hey everyone, I hope this is the right place to put this. I was wondering if you could answer this question. Basically, I'm having trouble with my Numerical Methods course. The only college-level math course I took before this was the Calculus 1 course. I'm wondering if because I hadn't yet...

I've got a problem where I need to numerically integrate a multivariable function but I'm not sure how to do this. I'm more than familiar with how to numerically integrate a single variable function numerically but I have no clue how to do this for a multivariable function. For example let's say...

Hey everyone, I'm starting a research project for my partial differential equations course, and I've chosen to research numerical solutions to the radial form of Schrodinger's equation. From some preliminary research, I've found information on using Numerov's method, but I am really not...

Homework Statement tan x = x Homework Equations The Attempt at a Solution how do i solve this equation without using graphs? is there a numerical method ? thanks a lot!

Hello there, I am taking a Numerical Methods course & i had a lecture today when we did an example on the 3-point formula to approximate the 1st derivative of f. the example included 4 given x's with their images by f. & we had to get all the images for the 1st derivative of f. so we...

Homework Statement Solve Fisher's equation u_t = u_{xx} + u(1 - u) numerically, with the initial condition (step function) u(x,0) = heaviside(-x) Homework Equations One can assume a traveling wave solution: u(x,t) = u(\xi) where \xi = x-vt such that u_{\xi \xi} = -vu_{\xi} - u(1...

not really math but wondering if someone is clever enough to know answer to this.. Some of you may know that if you pick (almost) any integer and add its reversed digits to it, and repeat this process ..you will eventually get a palindrome. for example: # 56 becomes palindromic after one...

Here's a simple numerical analysis problem that is confusing me. Can someone help me understand what boundary conditions to use here? f''(x) - (x^2 - E_n) * f(x) = 0; Assume f -> 0 as x -> +- inf. This equation comes from Schrodinger's equation for a one dimensional trapping potential...

I have a technical question about numerical relativity, hopefully someone can help. In the usual 3 + 1 decomposition in NR, the four gauge freedoms are expressed via the lapse, \alpha and three shift components \beta^i . In a finite element numerical scheme, each grid point will have a value...

I have a field ,B, I need to find the other field,A, such that -> __ -> B = \/ x A I need numerical solution, given B sampled on a 3D computational grid (finite difference hexahedra) find A. What numerical methods could be used?

\int^{1}_{-1}f(x)dx = \sum^{n}_{j=-n}a_{j}f(x_{j}) Why does \sum_{j}a_{j} = 2 ? I know that the aj's are weights, and in the case of [-1,1], they are calculated using the roots of the Legendre polynomial, but I don't understand why they all add up to 2.

Hello, after having used Scilab for the longer part of a while by now, I'm looking to change over to a functionally more enhanced software but am not yet sure which to choose. I've more or less come down to a choice of four programs, of which I would like you to pick the one which you think is...

where could i find the pseudocode for Newton raphson's method according to the MATLAB program??

Homework Statement a. Using equation x2 – a = 0, show that x_{n+1}=\frac{1}{2}\left(x_n+\frac{a}{x_n}\right) b. Given that Xn = √a + e, where e is a small error. Show that: x_{n+1}=a^{1/2}+\frac{1}{2}\left(\frac{e^2}{a^{1/2}+e}\right) c. If x0 = 4 and a = 7, where √7 = 2.646, find...

Numerical Methods/Diff Eq :) 2. Problem Clarified: Solving for v(t) Homework Equations equation (1) The Attempt at a Solution I know the two parts of the hint are important, and tried moving the dt over to the other side and integrating, but I can't seem to isolate the velocity. I think...

In EM scattering problems in inhomogeneous (layered) media one may encounter Sommerfeld integrals of the form: \int_{0}^{\infty}J_{n}(k_{\rho},\rho)k_{\rho}^{n+1}G(k_{\rho})dk_{\rho} where J is a Bessel function and G is a spectral Green's function, \rho is source-observer distance and in...

All matrices A\in\mathbb{C}^{n\times n} have at least one eigenvector z\in\mathbb{C}^n. I'm interested to know what kind of algorithms there are for the purpose of finding an eigenvector. I noticed that \frac{|z^{\dagger} A z|}{\|Az\|} = 1\quad\quad\quad\quad (1) holds only when z is an...

I hope this is the right place to post this question. I'm trying to figure out how to run a numeric integration for a nonlinear second order ODE with Neumann B.C. I've started programming up Runge Kutta 4, but clearly without a boundary condition on the function, but only on its derivative...

Homework Statement Proff that f´(x) = the lim of delta x approaching to 0 of f (a + delta x) - f (a -delta x) / 2 delta x Homework Equations The Attempt at a Solution the book hinted me that I should solve it in this way f (a + delta x) - f (a) + f (a) - f...

I have system of first order ordinary diff equations, indipendent variable is x cordinate. I know asymptotic solution in left and right region (i.e. when x->-infinity or x->infinity, e.g. when abs(x)>1000), it's const plus exponentially falling function. I want to find numerical solution in...

Homework Statement I'm trying to do some numerical stuff with vibrations of H20 and I'm working in mdyne, angstroms, atomic mass units, and angles are given in radians. What would the corresponding unit of time be when I calculate my normal mode frequencies? femtosecond, 10e-15?

I want to integrate a function in 3D space, and then plot the integrated function, to compare with my analytical solution, I am using Fortran 90, I have no problem integrating, I am just not sure how I can plot the resulting function out. I am currently thinking about piecewise integration...

hello, i'm wondering is there any review of most used methods in magnetostatics? and also if there are analitical solutions of distibution of magnetic field in cylindricall coordinates for: current loop, solenoid, current flown cylinder, coaxial cable and magnetic buffer (protection)...

Homework Statement I have a function that attempts to imitate the internal forces of the cord used for bungee jumping. I have been told to resolve it using Runge-Kutta 1st order numerical aproximation, therefore i have to reduce it to a system of equations. The preffered Runge-Kutta method...

Question a stone is thrown vertically upwards. if it takes 30 seconds to return to the ground, How high does the stone go?.. I need asap solution

Homework Statement Use the composite trapezoidal sum rule to evaluate I = integral from 0 to 1 of: (exp(x)-1)/x At x = 0 the integrand evaluates to 1. Select the step size h in order to guarantee an approximation error less than 10e-5. Carry out your calculation with at least 10 decimal...

hi, i would need some info on how can implement in MATLAB or FORTRAN (g90) the Numerical evaluation of the integral \int_{-\infty}^{\infty}dxf(x)exp(iux) and the evaluation of the ivnerse Fourier transform \int_{-\infty}^{\infty}du\frac{F(u))}{\int_{-\infty}^{\infty}g(x)exp(iux)dx}...

Some disasters attributable to bad numerical computing http://www.ima.umn.edu/~arnold/disasters/disasters.html That's why software QC/QA are critical - both in the code/method and in the implementation/application. And not to forget: Garbage in = Garbage out

Homework Statement If T is a linear transformation on the finite-dimensional inner product space over complex numbers and is normal, then prove that the numerical range of T is convex. Homework Equations The Attempt at a Solution If we assume a and b are in the numerical range of...

Please someone help me how to find information about the advantages and disadvantages of each method (Euler, Heun and Runge-Kutta). I surched in google and there is nothing useful posted there. We using Dennis Zill textbook for First course of DE. I need to kind of compare them before I use one...

Hi all. I need a book on advanced numerical methods (note: methods, not analysis) suitable for an undergrad. I have already had a first course in numerical methods, the usual one an undergrad takes. The topics the book needs to cover is: Finite difference, finite elements and spectral...

If I have a vector of data that is equally spaced in time. What is the best numerical method for integrating this data?