Numerical Definition and 701 Threads

This isn't so much of a homework problem as a general question that will help me with my homework. I am supposed to prove that a given function is uniformly continuous on an open interval (a,b). Since for any continuous function on a closed interval is uniformly continuous, I am curious...

ok, I'm not completely sure which section this goes into, but since I'm using this to solve a PDE ima going to put it in here, I need to integrate w(x,y,z)*V(x,y,z) over a cylindrical domain, it would be fairly simple if V had a "formula" describing the function, but i only have V as a number...

Homework Statement An object of mass m falls from rest at a point near the Earth's surface. If the air resistance is proportional to the velocity v^2, the differential equation for the velocity as a function of time is given by m*dv/dt = mg - cv^2 For the given paraments g = 9.81 m/s^2. m...

Hi, For a small problem I'm working on in quantum field theory, I have to numerically evaluate the integral \int_{-\infty}^{t}du e^{i\omega u}erf\left(\frac{u}{\sqrt{2}\sigma}\right) where erf(z) is the error function. Now, I have to replace -\infty by some large negative number, so...

Hi guys, I am looking to integrate the attached equation using C++. I was wondering if you could tell me what type of equation it is, and if you could recommend an algorithm to use to solve this (and why)? I need to use this for 100's of points (m,n) on a grid so a fastish algorithm...

Please, I am new in MATLAB and need some help as to whether MATLAB can perform this integration, and how to go about it. I have tried 'quad', 'quad8', 'trapz' and even a sum approach but it returns either a not-a-number answer or mtimes error or mrdivide error message. What I want to do is this...

Homework Statement Assume the spring force of a bowstring acting on an arrow does not follow Hooke’s Law because the bow’s material becomes more rigid as it is drawn back. The string’s force as a function of the drawback distance in meters is: F(x) = -k1x -k2x|x| where positive x is along...

Discrete Mathematics -- Symmetric Closure Math help in Numerical Analysis, Systems of I can't seem to find the way to approach this problem. Because it has symbols I don't know how to type here, I have attached an image here instead. Please help me if you can. Any input would be greatly...

Hi all, I have a function defined by an integral containing an arbitrary real parameter q. I can't do the integral, so I wanted to plot the function by evaluating the integral numerically. However, I can't do this owing to the arbitary-non numerical parameter in my integrand! Can anyone tell...

Hello there! I am solving a heat diffusion problem which is described by the differential equation: θΤ/θt=a*(θ^2Τ/ΘΤ^2). I will apply two diffrent temperatures on the ends of a metal rod. Solving the equation i conclude, according to the boundary conditions of course, at the function...

Homework Statement Plot the following parametric curve, defined by the following two polynomials, on the interval: t \in (-1;1). What shape do you get? x(t) = 16243t^{14} + 520143t^{13} -798515t^{12} -185877t^{11} + 150142t^{10} + 256559t^9 -135331t^8 -170995t^7 + 594415t^6 + 558842t^5...

I've written a Levenberg-Marquardt nonlinear optimization routine that employs the reverse-mode automatic differentiation algorithm for building the Jacobian. So far it has worked marvelously for me. However, now I have to use functions that contain integrals that cannot be analytically taken...

Homework Statement K(max) = (6.63x10^-34 J s)(7.09x10^14s) - 2.17x10^-19J solve for kmax Homework Equations none? The Attempt at a Solution K = (6.63x10^-34 J s)(7.09x10^14 s) - (2.17x10^-19 J) K = (6.63)(7.09)(10^-34)(10^14) J s^2 - (2.17x10^-19 J) K = (47.0067)(10^-24) J s^2...

Being a hobbiest programmer, I know enough about probability to get by. However, I've set myself an impossible (for me) calculation in my current personal project. I have a set of numbers. For this particular problem it is a set of four numbers {248, 184, 120, 56}, but I'll be repeating the...

Consider a new computer system which stores data in “quads”, i.e. it has four states 0, 1, 2 and 3 (as opposed to binary which has only two, 0 and 1). Now imagine that numbers are stored in a 12 quad format where there is one quad for the sign of the number, three quads for the exponent...

Hi! I have to solve a system of two coupled nonlinear ordinary differential equations. In the function that defines the system there are terms with square root of the dependant variables. I tried to solve the system numerically but in the nmerical solution I get violent oscillations. Then I...

Good evening, I have a background on one-variable Calculus and I am currently self-studying Calculus from Leithold's "The Calculus with Analytic Geometry". When I finish the part about infinite series, I plan to start studying Numerical Analysis. I would like to ask what book on Numerical...

I am kind of new to mathematica, and have checked the documentation but can't seem to find an answer. I have solved 3 coupled differential equations using NDSolve. I wish to integrate the solutions over a range but I'm not sure how to do it - the documentation seems to deal only with...

First of all, I apologize if this is in the wrong section. I would like to know what background is needed to be properly prepared for numerical analysis. I will have had calculus III (leaving C-4 left), ordinary differential equations. I'd be taking linear algebra concurrently. Also...

Homework Statement Well, I'm not sure if this is a correct subforum to post my problem, but to me it does seem to me as an academic problem. One I can not solve, apparently. Well, anyway. I'm solving the 1+1 radial wave equation using finite difference. I shifted my grid, so that the origin...

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

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...

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...

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 ...

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...

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...