Numerical Definition and 775 Threads

They say this is just by chance. But maybe some bright spark has come up with a mathematical derivation for it? Alternatively, what about simulating the cloud of the early solar system on a computer. Would the Titius-Bode pattern of the planet distances arise? Here's the law...

Hi, I have to solve (using numerical methods) fallowing problem: there are for example three pointed bodies in 2D. I have to find trajectories of their motions in their own gravitational field. In cartesian coordinates for each body and direction I write equation of motion (that gives me system...

Pliz Help me and enlighten me about the numerical and non-numerical applications of computers.

Hi! Is it possible to solve the following problem in MATLAB or maple? {d(phi)/d(lambda)}^2 = (sin(phi))^2 - (sin(phi_one))^2 I need to determine phi_one numerically given the following boundary conditions: phi(0)=C1 (constant) and {d(phi)/d(lambda)} = 0 when lambda = C2 (constant)...

Hi! I need help from someone that knows something about numerical methods in MATLAB. Specifically, fsolve. So, I have an equation L = K(x) - F(x,y). Given the values of L and y, I need to determine the value of x numerically. So, here's what I've done: G(x) = L- K(x) + F(x,y) in the...

Given any distribution of mass, the gravity at any point outside it can be calculated by dividing the mass into infinitesimal masses, and adding up the gravity due to each. Doing that, I faced a problem on the surface of an object: no matter how small you make the integration step, near the...

Hello to all! Homework Statement for testing my program i need a heat equation with numerical initial and boundary conditions: Derivative[2, 0][f][x, t] == Derivative[0, 1][f][x, t] f[x, 0] == numerical f[0, t] == numerical, f[numerical, t] == numerical PS. to moders: please, if...

does anyone know a good book that will help with 'Numerical Methods' at university level? thank you

Hi all. Can someone briefly explain the difference between finite difference methods and spectral methods? What are their principles? And what is pseudo-spectral method?

I need 1 of the following 2 Numerical Methods books. Can anyone advice me which one do you think is best? Numerical Methods for Engineering Application, 2E Joel H. Ferziger ISBN 0471116211 John Wiley & Sons Numerical Methods, 3E J. Douglas Faires, Richard L. Burden ISBN 0534407617...

Hello, Any ideas on how one would go about attempting to solve this set of equations (for x and y and lambda) without numerical methods. Is it possible, even just to get a approximate solution? Is a set of two 2nd order DE's, \ddot{x} - \dot{x} + xy/R - y^{2} tan(lambda) -...

IM given a question on MATLAB programming. It ask to construct a numerical generative model for autoregressive model of order two; xt -xt-1 + 0.5t-2 = et. generate and plot 256 time series samples. then numerically obtain the spectrum of this time series and plot them. assuming noise process...

Homework Statement take the rational function R(x)=(a+bx)\(c+dx). What does the interpolatory requirment R(xi)=yi, i=1,2,3,4 amount to? under what conditions can you find coefficients? uniquely? Homework Equations The Attempt at a Solution Let y=[y1,y2,y3,y4] and v=[a,b,c,d] and...

Hi, I am trying to numerically calculate the tunneling probability for a wave function |psi> as a function of x. I have a double well potential. The wave function is initially in the left well. I do not know what exactly I have to find to show tunneling: the probability of being on the left well...

I have three equations (\frac{\partial}{\partial t} + c \frac{\partial}{\partial z}) E_p(z,t) = i N_r(z) \sigma_{ba}(z,t) \frac{1}{i E_c^*(z,t)}(\frac{\partial}{\partial t} + \Gamma_{bc}) \sigma_{bc}(z,t) = \sigma_{ba}(z,t) -\frac{E_p(z,t)}{E_c(z,t)} + \frac{1}{i...

Homework Statement Hi! I'm studying a computational physics course and have been ok so far but the newest problem relates to quantum mechanics and I am struggling to understand... I would really appreciate it if someone could help me . i want to solve the Heisenberg hamiltonian for 10...

there are 5 examples as follows: %%% example01 %%%% z=linspace(-0.1,0.1); a=0.1; kesi=(z+sqrt(z.^2-a^2))./a; for j=1:length(z) f=@(b) log(1-((b+sqrt(b.^2-a^2))./a)./kesi(j)); I(j)=quadl(f,-0.1+eps,0.1+eps,1e-8); end %%% example02 %%%% z=linspace(-0.1,0.1); a=0.1...

Can anyone tell me what is the equation for First Order of Newton’s Interpolation? The one of Interpolation I know is Lagrange’s Interpolation such as p(x)= \frac {x-x1}{x0-x1} f(x0) + \frac {x-x0}{x1-x0} f(x1) and so on ... Thanks in advance

Let g(x)=(x-x1)(x-x2)(x-x3) -1<=x1<x2<x3<=1 find the points x1,x2,x3 so that max |g(x)| for x an element of [-1,1] is as small as possible. This is the only problem I have left and I have no idea how to do it. We've been covering Newtons method and rootfinding but I don't think it...

Hi, I'm currently stuck with 2 questions: 1. Given that the negative root of the equation f(x) = x^{3} - 7(x) + 5 lies between a and a + 1 where a is an integer write down a value of a 2. Show that the equation e^{-x} = x^{2} has a root between x = 0.70 and 0.71 Thanks :)

Do you know of code (preferably C/C++) to do this for non linear least squares? i found a program called levmar on the internet, but it seems inadequately documented on how to use it and probably not so useful to my purposes. My problem is evaluation of a carpet. The middle is worn out and it...

Hi I need help with a question in a Fire Safety course I'm studying for. The question reads : Define the following terms and indicate the units in which they are normally expressed. State how low numerical values for these properties would affect the ease with which solid materials can...

Hey everyone, Ok, my ultimate aim is analysis of gamma ray burst light curves, so i have data which includes count rate in a certain energy range recorded every 64 ms. I would like to apply some kind of discrete, numerical Fourier transform to this long list of data, in order to produce a new...

Dear every memeber, I encountered the numerical computation on the following differential equations. I use four-step Runge-Kutta methods to integrate, but the result is not converge, even if I take the time step (t=0.0001). please help me why so? Could you please tellme which Fortran...

2 Questions

Ok, I'm trying to recreate some results from a paper, and I am really lacking in understanding. I'm getting extremely frustrated. I'll try to create a similar problem that replicates the original problem. The original problem, is three coupled non-linear differential equations that must be...

Homework Statement log_u (5) = a; log_u (27)=b; log_u(32)=c what is the numerical value of u^(2a+(1/3)b-(2/5)c) Homework Equations The Attempt at a Solution Can you do (u^2a * u^(b*1/3) ) / ( u^(c*-2/5))) and then do log_u of the whole thing from here can you make it ((u^a)^2 *...

This is for a computer project and the questions asks to compute a sum from J=1 to n of 1/j^2 from smallest to largest... i.e. (1/n^2+ 1/(n-1)^2+...1/9+1/4+1) for n=10, n=100, n=1000, n=10000, and n=100000 Is there i way i can do this in my calculator? or is there i command i can use in maple??

Can anyone here give me the examples of most test problems of Numerical Methods in the Mid and End of semester at undergraduate level? What is the most test problems of Numerical Methods in the mid and end of semester at undergraduate level that probably must come out in the test? I am...

I think I have returned all my math back to teachers without any refund. y=f(x); h=xb-xa, which is very small. My Q is to calculate curve length rather than area numerically. But let me use area as example to show you what i want. to calculate area between xa to xb, we have 2...

Hello, the work I am doing now requires numerical solution of several reaction-diffusion equations such as the standard advection diffusion equation (ADE) or IE Fisher's equation. So far I have been using the only method I am familiar with, the simplest one I believe: to express the time...

Does the Simpson's rule of numerical integration (\frac{1}{3}h\left( {f_0 + 4f_1 + f_2 } \right)) give exact values for all polynomials to a third degree i.e., linear functions, quadratic functions, and cubic functions? Is there a better method for numerical integration approximation? One...

Hi all. Could you please recommend some nice books on numerical approach to NLS or introduction to NLS in general? I don't have a strong background in numerical methods nor any prior knowldege in NLS or quantum mechanics. So, perhaps an introductory book would be suitable at this stage. Thanks.

It seems that understanding numbers in physics is often almost as important as understanding concepts, specifically when approximations to equations are made. But I found myself lacking in intuitions in these numbers... When my professor is lecturing, he always gives out numbers. for instance...

I'm sure everyone here has seen one of these things some time or another. Where you're given something like... SEND +MORE ______ MONEY ...and then you have to figure out what each letter represents as a number in order to make the solution make sense, and no two letters can equal the...

For example, in tight binding model, the site energy is random I want to have 100 disorder realizations, then I have the following two questions: 1. Do different realization needs different seed in the random number generation subroutine? 2. When all realizations are completed, the...

I am trying to understand how they find an exact solution of Einstein equation and the field equations for the matter fields. My problem is that in GR the coordinate system cannot be chosen independently from matter from the very beginning like in Newtonian mechanics. For example, in...

Homework Statement Consider a symmetric matrix, A, n x n with distinct eigenvalues lambda_1 > lambda_2 > ... > lambda_n (note: i didnt miss anything here typing this, there are no absolute values here). What value of the shift beta will give fastest convergence to lamba_1 and its...

Homework Statement Given the system x'(t)=-ax(t)+ky(t)+g y'(t)=lx(t)-by(t)+h If g=h=0, a) Find the equilibrium b) Show that if ab-lk does not equal 0, the steady state found in (a) is the only solution c) choose a,b,l,k such that ab-lk > 0. Find numerically the solution of the system...

a "C" problem is anybody aware of numerical methods in C language... numerical methods include Newton-Raphson method,Euler's method,Milne's method,Newton's forward and backward implementation,Gauss divergence backward and forward interpolation. pls help me,i will b so thankful 2 them who...

I figured it out. Thanks!

What is meant by " a numerical method to solve a three body problem?"

Can you tell me what Numerical Analysis is? I wonder if this is good for a Physics major to take?

Hello, I would be interrested to learn if there are some (new) open source and/or possibly free librairies available for nonlinear optimisation and equations solving. I would be mostly interrested in modern languages like java or C# . "Clean" fortran could also be interresting as long as...

Hello, I would be interrested to learn if there are some (new) open source and/or possibly free librairies available for nonlinear optimisation and equations solving. I would be mostly interrested in modern languages like java or C# . "Clean" fortran could also be interresting as long as...

I'm trying to decide what programming language I should learn for computational aspects of my research. Right now, I've boiled it down to learning either C or Python. I know C is ungodly fast, but I've heard Python is quick to code and has a huge scientific library. Anybody able to help me...

When Newton wanted math to express his physics he invented calculus (i'm not trying to be totally historically correct - this isn't my main point). It seems like today we're in a similar position - there're lots of things that simply can't be exactly solved. are numerical methods the next...

For starters... What does "data reduction" mean? The book starts throwing around this term (which is also part of the book's title) without even defining it. homework question: Show by numerical calculation that, for the Gaussian probability distribution, the full-width at half maximum...

Homework Statement In Matlab, Find the scalar (lamda) for which x+(lamda)v equals the solution obtained with the backslash operator \. Hence, x=B\b in matlab (This is another way of finding the inverse inv(B)... we could also use x=B\b) Homework Equations We have Bx = b B =...

Homework Statement This problem is about solving an equation system numerical using lipschitz method or whatever the name is. x_1 = sqrt(1-x^2) x_2 = sqrt((9-5x_1^2)/21) and we create (x_1,x_2) = x g(x) = (x_1,x_2) (fixed point equation) lipschitz states: ||x^(k+1) - x^*|| <=...