Numerical Definition and 701 Threads

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...

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...

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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...

we've a basic numerical integration assignment, using simpsons/trapezium rule to calculate some non analytical function. Logic suggests that you use as many "strips" as possible (ie. as small a value of dx as possible) to estimate the value of the integral, however I've seen some graph some...

using composite trapezoidal rule with n=4 how can i get a bound for the error of I=integration tan(x) from x=0 to x=pi/2 i know that the term of error in comp trapezoidal rule is (b-a)/12 h^2 f''(eita) i got the second derevative of tanx to be 2sec^2 x tanx then i don't know with what value...

Hello, For Euler's Method of Numerical Approximations, my book (Boyce&DiPrima) gives this algorithm: Step 1: define f(t,y) Step 2: input initial values t0 and y0 Step 3: input step size h and number of steps n Step 4: output t0 and y0 Step 5: for j from 1 to n do Step 6: k1 = f(t,y)...

Hey all :smile: I have a house mate is doing a computer physics course and he's never before dealt with matrices bigger than 3 x 3. He was wanted to know out how to work out the inverse of 6 x 6, now it's been a long time since I've done this myself. I remembered the Gauss - Seidel Method...

in Newton forward differece method. how can i know that i reached the best interpolation? for example in a function like sqrt(x) for Xi=1,1.05,1.10,1.15,1.20,1.25,1.3 the best interpolation is at P3(x) why?how can i know? this really makes me conused:confused: :confused: if anyone...

A 5kg block is resting on the top right hand corner of a 10kg block. The length of the top of the 10kg block is 10m. Find the time taken by the 5kg block on top to slide of the 10kg block completely if the 10kg block is accelerating at 5m/s^2. My work: aB = accleration of the 5kg block aA...

Hello could someone give some info about the "Numerical solution" to GR...is this a field of "Computational Physics"?.. - What i know is that you take the Hyper-surface, and you " split " it into triangles..and use the ¿angles? of every triangle as finite-coordinates..then you get a problem...

Anyone got suggestions for an AP Calculus textbook? Hello, as the title says anyone have suggestions for a good, easy to understand textbook for AP Calculus? Thanks PS: This thingy below is what troubling me... our school has an sucky textbook for this course, so confusing...

Hello, I'm trying to construct a code in determining the Asymptotic Error Constant and the order of the rate of convergence, r for several iterative methods like the Fixed point, Newton Rhapson, and Secant methods in determining roots, using Scilab 4.0 (which is said to behave much like...

Can anyone point me to a website or set of notes that I could read up on the topics of this course? course includes: solving for the roots of algebraic and transcendental equations, solution of simultaneous linear equations, least-squares curve fits to data, interpolation, numerical...

Are there many interesting computational physics problems out there? Are there any comet trajectories that will deviate from a standard ellipse? For some reason plotting the path of a baseball just doesn't spark my interest.

This is a developing area in the nuclear industry involving large scale multiphysics computation. For the past several years Argonne National Laboratory and Purdue University have been supported by the Department of Energy (DOE) and the Electric Power Research Institute (EPRI) to develop a...

(I am not sure whether I'm posting in the right forum. I apologize if I do) Does anyone have an alrorithm or a code (in any language) that constructs a Poincare surface of section? I want to do so for a Hamiltonian model: A mass under the influense of the Henon-Heiles potential. It has to...

I have a quick question. For a project that I'm doing, I need to numerically solve systems of nonlinear differential equations. Can anyone suggest a numerical method which I could code as a short C program? Thanks.

Hi all! I am coming back here after a long time. Last time I got the answer I was looking for, here. I hope that I will find it again. I need the possible numerical methods for solving the following PDE: Its a nonlinear parabolic boundary value problem. I want a very stable algorithm as...

I have been given the following problem as assignment: Find a numerical solution for the 1-D heat conduction (using the Explicit Method): \left\{\begin{array}U_{xx} = U_{t},\\ U(x,0) = \sin \pi x, \\ U(0,t) = U(1,t) = 0 Use h = 1, k = 0.005125 and M = 200. Can anyone help by giving...

I am a geology major interested in groundwater modeling. Currently taking ordinary differential equations, and I'll be in a computational numerical methods course for engineers next fall. Here is the course description.. "Introduction to numerical methods for environmental engineering...