Numerical Definition and 701 Threads

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 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...

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...

Hi, I have the following problem. I am tried to numerically solve the 1D heat equation for a metal bar of length L. Using the forward time, centered space equation a(t+1) = a(t)+(alpha*deltaA/(deltaX)^2)*(a(x+1,t)-2*a(x,t)+a(x-1,t)) The problem is that I only have ONE heat source at...

I am trying to plot the following numerical solutions: Input: NDSolve[{y''[x] + (2/x) y'[x] + 1 == 0, y[10^(-10)] == 0.9999999, y'[10^(-10)] == 0}, y, {x, 0, 30}] Output: {{y->InterpolatingFunction[{{3.34649*10^-105, 30.}},<>]}} But when I plot it, I just get a completely blank...

Homework Statement "Estimate the mass of water in all the World’s oceans." Homework Equations I know the following: Two-thirds of the Earth is sea. The density of seawater is 1025 kg/m3. Radius of the Earth = 6.3*106m. The Attempt at a Solution Let's assume that the...

Homework Statement This is a problem in numerical estimation. Estimate a typical maximum momentum pmax for the free electrons in a metal where pmax = \left(\frac{3nh^{3}}{8\pi}\right)^{1/3} (In estimating n, the number density of free electrons, assume there is one such electron...

can anyone provide a Numerical algorithm to solve -y'' (x) +f(x)y(x) = \lambda _{n} y(x) with the boundary condition y(0)=y(a)=0 here 'a' is a parameter introduced at hand inside the program and f(x) is also introduced by hand in the program i am more interested in getting...

From the attachment. i would like to know how to find (t_1 and t_2)minimum if given t_0=0 and t_3=5.It seem like when using excel solver to find the minimum.anyone know how to do it with mathematica?

i have problem regarding to the numerical method. my problem is from da attachment,if i replace x with value 1,it will get da answer by using NIntegrate.I want to know if i can get the value of t_minimum from the answer.thanks a lots.

Homework Statement 13. A box of mass m is released from rest at point A, the top of a long, frictionless slide. Point A is at height H above the level of points B and C. Although the slide is frictionless, the horizontal surface from point B to point C is not. The coefficient of kinetic...

some one help me to solve these questions. 1. The order of convergence of Newton-Raphson Method is a) at least one b) at most two c) at least there d) four e) none of these. 2. Newton-Raphson Method fails to find the root of f(x)=0 if: a) f'(x) > 0 b) f(x)< 0 c) f'(x) = 0 d) f'(x) <0...

Good afternoon, I'm willing to study (teach myself) http://en.wikipedia.org/wiki/Numerical_analysis" , which I find very interesting, and which seems to be very useful for solving Physics problems (specifically, the motion of celestial bodies). I have a background in Calculus (basically...

i want to find the minimum sum of this equation and find the t like using solver in Excel,but since the integration cannot be integrate directly,i didnt know how to use the numerical integration to apply for this problem. i want to find the value :let say when n=2, t_0=0 and t_n=1, so i need...

Hi, I've using numerical integration method (Simpson rule) to evaluate a definite integral in the interval [a,b]. I was wondering what is the ideal way to approximate the integral in the boundary [a,b) or (a,b] or (a,b) when for example, the function inside the integral does not exist at that...

Hello to all I've been wondering about the skills needed for doing a research degree. I've been looking at the Matlab language recently and it seems somewhat similar to Java. Is Java just as easy to use as Matlab for doing numerical methods? I'd be interested in hearing your views. Thank you...

hello, I have a problem with the use of quad function in Matlab for numerical integration. Let me try to explain on an example. When I want to find the integral of expression exp(-x^2/2) from 0 to infinity, where for the higher bound I use some very large number: Q =...

Hi, can anyone tell me how to add a text line in the numerical solver calculation screen that describes a variable in an equation? for example spl = 20 log (D2/Dr) Dr is a reference distance from a source D2 is a prediction distance I want some form of description of the variable...

http://i48.tinypic.com/2yzd213.jpg how they got g1 g2 g3 ?

Homework Statement I am using Crank–Nicolson to solve a logistic function, modeling population growth. To get the next time step, I have to solve a quadratic equation. The problem is that i get two solutions for y(i+1). Does it mean that I am doing it wrong? If not, can I just pick the...

Hi all, I have an ODE with the form \frac{\mathrm{d}^{2}\phi}{\mathrm{d}x^{2}}+a\exp(b\phi)=0 B.C. \frac{\mathrm{d}\phi}{\mathrm{d}{x}}\right|_{x=0}=-c,\frac{\mathrm{d}\phi}{\mathrm{d}{x}}\right|_{x=L}=0 where a,b,c,L are all positive. I solved the problem with Maple using the dsolve...

Hi, I noticed such a strange behavior in my code every time I add a threshold: little oscillation around the threshold value itself. For example f(x) = g(x), x > x_c f(x) = 0, x <= x_c \frac{dx}{dt}=f(x) I solve the last equation and I find this oscillation. Can they be removed?

i am very new in matlab. and i need to calculate the arc lengh. My equation is arc length = integration of sqrt(d.*(k.^2-2).*sin(k.*t./2).^2 - d.*(k.^2-1).*sin(k.*t./2).^4 + 1); from 0 to 2.pi where, d=(0:.1:1) and k=(0:1:10) can anybody tell me whether it is possible to calculate this arc...

Please help me with this problem! I have no clue. I know how to deal with only dy/dx. But this includes dy/dx and dz/dx...:cry: Please see the attachment :) Step size h = 0.2 range x = 0 to 1 y(0) = 2 z(0) = 4 Thank you, Maya

Homework Statement Using the Schroeder-Bernstein Theorem, prove that any two intervals of real numbers are numerically equivalent. Homework Equations Schroeder-Bernstein Theorem: Let A and B be sets, and suppose that there are injections from A into B and B into A. Then, there exists a...

Hello I have a function which is very similar in shape to a Gaussian, except it is not a distribution and it is not analytic, so I can at best calculate a single point on the curve at a time. (In general it is a convolution of different distributions but this is not important). I need to find...

Homework Statement Consider the half space defined by H = {x ∈ IRn | aT x +alpha ≥ 0} where a ∈ IRn and alpha ∈ IR are given. Formulate and solve the optimization problem for finding the point x in H that has the smallest Euclidean norm. Homework Equations The Attempt at a...

help me please "numerical method" please help me finish college assignment, I was given the task of creating programs numerical calculation method, the bisection method, the program c + + or Visual Basic, or any program language. last collection time Friday, 23 April 2010. please help me...

I have an assigned project in Physics with numerical modeling, to which I am supposed to use Euler's method to approximate the velocity of a "mass sliding down a frictionless in the shape of a quarter circle of radius 2.00 m." The assignment also states: "Do three trials: t = 0.2s, t = 0.02s...

in this page http://i40.tinypic.com/seyrys.jpg we can't see what is the pattern of finding s? what s represents? in iteration 0 s is found by sum of an and bn in the 1st 2nd and 3rd iteration its found by their subtraction in the 4th its neither ??

i know the law (fg)'=f'g+fg' but here there is epsilon and it turns to someother sign i don't know what it says. i can't understand the transition ?

how to do those tables of calculation in math lab i got sum really long formullas in other question and if ill do the itterations i will spend half a day just on that

When can we expect to see numerical simulations of GR for cases that are not highly symmetric? Say 10^3 blobs of matter in an arbitrary initial configuration.

y=\sqrt{x^2+1}-1 how do we know that there is a subtraction of two close numbers thus making loss of significance? there is no close numbers there is variable X it could give use a close result or otherwise and why multiplying and dividing by y=\sqrt{x^2+1}+1 makes it go away?

Im using the c programming language and just wanted to ask a quick question. In a while loop how do you make the program terminate by printing a value or a message here's my code while ((fabs(func(x))>epsilon)) { if(deriv(x)==0) { print the last value of x and stop the whole program} else {...

Hello-- I need to generate synthetic data to test an algorithm used to process data from an experiment. A synthetic wavelet is constructed using the following equations, but I am uncertain how to numerically evaluate the improper integral shown below. \[ u(t) = {\mathop{\rm...

Homework Statement If x is a real number, we define [x] as being the largest integer <= x. For example, [1.2] = 1, [-1.1] = -2, [1] = 1, [11/3]3 = 3, . . . Let {an}n>=1 be the numerical sequence defined by: a1 = 3; and an = a[n/2], for n>=2 (a) Give the terms a1; a2; ... ; a8 of this...

Homework Statement Solve the differential equation \frac{dy^2}{dx^2}=xy^2-2yy'+x^3+4 where y(1)=1 y'(1)=2 by means of the Taylor-series expansion to get the value of y at x=1.1. Use terms up to x^6 and \Delta x=0.1The Attempt at a Solution I'm unsure as to how I should go about...

Homework Statement For fluid flow in pipes, friction is described by a dimensionless number, the Fanning friction factor (f). The Fanning friction factor is dependent on a number of parameters related to the size of the pipe and the fluid, which all can be represented by another dimensionless...

u''(x)=f(x), boundary conditions u(a)=0,u(b)=0. (u(x+h)-2u(x)+u(x-h))/h^2=f(x); maltab code: clear all a=0; b=1; n=10; h=(b-a)/(n+1); x_with_boundary=linspace(a,b,n+2)'; x=x_with_boundary(2:n+1); A=h^(-2).*(diag(ones(1,n-1),-1)+diag(-2.*ones(1,n),0)+diag(ones(1,n-1),1))...

Hi, I was wondering if anyone can point me to a general treatment of errors when doing numerical integration of measured variables? My problem is that I am integrating force with respect to displacement (of a piston) in an attempt to calculate work...and getting some impossible numbers...