Numerical integration Definition and 140 Threads

In my computational physics textbook, three different velocity estimators are derived for a problem with equation of motion: \ddot x = F(x) where the positions are found by using the Verlet algorithm: x(t+h) = 2 x(t) - x(t-h) + h^2 F[x(t)] The three velocity estimators are: v(t) = \frac{x(t+h)...

Dear All, Can someone suggest me an appropriate routine (in Fortran) or command (in mathematica) to perform numerical integration of a function, which is specified numerically on a one dimensional grid with equal spacing (and we cannot generate additional data on other grid points)? There are...

I need to compute numericaly n-body sys. interacting acording to the Weber force: http://en.wikipedia.org/wiki/Weber_electrodynamics and I have a problem with the acceleration on rhs: r'', because the acceleration is unknown, due to the Newton law: F = ma, and we need just 'a' to do next...

Hi, I need to calculate area of an irregular polygon which can be of any complex shape numerically i.e. using numerical integration techniques. Please can anyone suggest any reference material / best way of going about this efficiently? Akash

Numerical integration methods applicable to a type of definite integrl Hey, so I've been working on a program to numerically integrate an integral of the form ∫xnf(x) dx, LIM(0 to INF.) Here n can go to negative non integral values, say -3.7 etc. and f(x) is a function of sin, cos and...

I have thousands of triple integrals with very ugly integrands to run. Each of those computations takes about an hour in R on a mediocre machine. For uninteresting reasons, when I was initially coding this up, that's the language and machine I had to work with. But now my options are wide...

Can anyone explain to me why the gaussian white noise term is multiplied by the square root of the time differential when we turn the Langevin differential equation into a finite difference equation for the purposes of integration? http://pre.aps.org/pdf/PRE/v50/i6/p4404_1 The step I...

Homework Statement This is for my computer simulations in physics class. The problem, as stated, is to numerically integrate a particular equation for a period of one year, given that the Earth starts at the point (1,0) with a velocity of (0,2pi). Then, I must plot the orbit. I am using Maple...

If I have a x,y table of discrete datapoints with a discrete dataset, such that delta x is not a constant, what are some of the more advanced techiques that I can use to integrate this? I remember that there were Trapezoidal rules and Simpson's rule where delta x IS a constant (and there are...

For this problem use Simpson's Rule with N=256 for numerical integration function is y=×^2 and the lower limit is 1 & 3 is the upper limit. I=\frac{h}{3} {fstart+fend+2Ʃfeven+4Ʃfodd} Find the numerical integration, using FORTRAN my solution follows...

Homework Statement Hi there, thanks in advance for any help! I have a first order DE: \frac{\partial \vec{m}}{\partial t} = -\vec{m} \times \vec{h}_{eff} + \alpha \vec{m} \times \frac{\partial \vec{m}}{\partial t} (a scaled Landau-Lifshitz-Gilbert equation) where m is a magnetism...

I have a plot with a bunch of data points. I would like to perform a numerical integration on it. I was just wondering, what method of integrating do you guys think would be best suited for a sinusoidal like curve?

hi all,,,, this is the integral that I would like you users work, I would like to know what methods and with all the steps as they arrive at the approach, I'm finishing a new numerical method to and I am doing some tests, to compare it with all methods made ​​by all users of this forum, and...

Hey I have taken a programming course. And I have learned about Simpson, Trapezoidal and the midpoint rule etc, I have programmed these. I have also implemented forward Euler, backward euler, Runge Kutta etc for solving ODE. I am wondering if there is any way to unify these two things, are...

I am struggling to understand interpolating polynomials and their errors. I have a problem off of a study guide here: http://terminus.sdsu.edu/SDSU/Math541_f2012/Resources/studyguide-mt01.pdf I understand that the composite simpsons rule is only exact for polynomials up to order 3, with error...

Hi, I have a mesh whose surface is made up of tesselating triangles. I would like to perform an integral over this surface of the form \int f(\Omega) R(\Omega) d\Omega Where f is an arbitrary function and R is the radius at that point. I have a method implemented but it is not working...

Hello everyone! I am trying to understand why the following function does not provide problems to being computed numerically: ∫dx1/(sin(abs(x)^(1/2))) from x=-1 to x=2. Clearly there is a singularity for x=0 but why does taking the absolute value of x and then taking its square root...

Hello, I am a PhD student in geology in need of help from a physicist! Can somebody spot the mistake in my spreadsheet? I am using an Excel spreadsheet (attached .xls) to integrate the Bethe formula in order to estimate the range (in cm) of alpha particles in quartz. I am using the version of...

I am intending to use Runge Kutta 4th order to numerically solve a system of coupled equations: \frac{d^{2}x}{dt^{2}} = K1 * x * cos(t) + ( (K2 * \frac{dy}{dt}) - \frac{dz}{dt} ) \frac{d^{2}y}{dt^{2}}= -K1 * y * cos(t) + ( (K2 * \frac{dz}{dt}) - \frac{dx}{dt} )...

\[2.37=\frac{1}{\sqrt{6}} \int_{0}^{x} \sqrt{\frac{e^x}{e^x-1}}dx\] please find x to three decimal point

I have a double integral: ∫∫sin^2(∏x/A)*sin^2(∏y/B)dxdy A=length along x B=length along y ranges: 0 to A(for x) & 0 to B (for y) Analytical result is: A*B/4 (unit^2) Now, I want to evaulate it numerically using trapezoidal rule. Infact, I have done it but not sure whether it is a right...

Wasn't sure where to ask this but here goes: Suppose one needs to work out the area under an experimental peak using numerical integration and every data point has an error in y. How do you go about providing a sensbile error on the integrated area? My current thinking is that the error in...

Homework Statement I need to find total distance traveled for an object using the speed profile which is the absolute value of velocity before integrating. so we finish up with the total distance travelled, rather than the final displacement from the initial position. And this is the...

Homework Statement Hey I Need Help With Numerical Integration: I Have Data Sets Which is Shown In The Picture Below http://imageshack.us/photo/my-images/69/numericalintegration.png/ Could Someone Use One of The Data Sets to Show Hows it Done Then i'll Do The Rest of Them Needed Answers...

So I have to numerically integrate a function that is quite difficult. I could post it, but its long. Regardless, there are 5 variables I am integrating over. The first is independent. The next 4 are subsequently dependent on the integration limits of the previous. Not a big deal. something...

good day all.i've just written a program in fortran77 for the model of a binary distillation column.i included a PI controller in my program.To obtain the integral term of the PI,I used the explicit euler to numerically integrate the error.i would love to compare my results using another method...

I have a symbolic function of three variables which I'm trying to numerically integrate wrt a single variable. Consider (syms x y a) and the function f(x,y,z). Here are some things I've tried, without success: 1. >>int(f(x,y,z),x,a,b) which analytically integrates f wrt x from a to b but...

Hi folks, I need to evaluate (numerically) a multi-dimensional integral of the form \int_A f(x) dx. Now in my application, I already have points inside the domain A which are distributed like \frac{f(x)}{\int_A f(x) dx}. So I hoped I could use these random points in some importance sampling...

Hi, I tried to numerically integrate an equation in MATLAB using the trapezium method. Here is the code that I wrote: ao = 1; X = 0:ao/10:ao; Y = 1/sqrt((power(Ho,2)*((O_m*power(X,-1))+(O_r*power(X,-2))+(O_l*power(X,2))))-(k*power(c,2))); age = trapz(X,Y); where the values for O_m...

Homework Statement Numerical integration using MATLAB m-files Find the area under the curve of: using trapezium rule Homework Equations g(x) = x^2 from x=0 to x=2 Area of a trapezium = h/2(a+b) The Attempt at a Solution

Find upper limit of improper integral -- Numerical Integration Hi, I have the following complicated integral willing to integrate numerically. The integral is: \int _0^{\infty }x\frac{\beta^\alpha}{\Gamma(\alpha)}x^{-\alpha-1}e^{-\beta/x}dx . We know that the integral converges to...

Would anyone please suggest the best numerical method for integrating complicated integrands and singular functions? I find that Gauss quadratures are suggested by many references but I can't find a method to obtain the abscissas and weights for a general function.

Help! Numerical integration in matlab So (assuming the period in a damped harmonic oscillator is constant, because it is right?) I have been asked to find T= 2* (integral from x1 to x2 of(1/v_num)dx) where x1 and x2 are two consecutive extrema (?? not sure what he means with this, i supossed...

Hallo, \Gamma(t) is a function that i can know only at dicrete points and appears in this integral: \int\Gamma(t) * tan (\Gamma(t)*t + \varphi) My question is now, which could be the best interpolation of \Gamma(t) that would allopw an exact integration? Thank you very much in advance

I have doubt in MATLAB How to integrate exp(x)*erfc(x) ? in MATLAB The warning msg it is displaying is : EXPLICIT integral could not be found

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...

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...

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...

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...

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...

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...

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!

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)...

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...

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.