Numerical Definition and 775 Threads

Why polynomials are used in numerical analysis?

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...

How do people generally determine uncertainties on results that are based on Monte Carlo simulations? Take this fictive example, just so we have something specific to talk about: I look at 106 particles, confined to a box. There is a small hole in one of the walls, and at some time t0 I am...

I'm looking for a good book on numerical methods. I know most of the basic algorithms but one that delves more into things like adaptive quadrature and that type of thing is what I'm looking for. Any texts people could recommend?

Homework Statement Consider an initial circular low Earth orbit act at a 300 km altitude, find the velocity change required to produce an elliptical orbit with a 300 km altitude at perigee and 3000 km altitude at apogee. Given gravitational parameter for Earth μ=398600 kg3/s2, radius of...

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...

Hey all, back with another question. I have the opportunity in the fall to choose 1 (maybe 2 if I'm lucky) of the following classes: Numerical analysis (undergrad numerical linear algebra, using matlab), Functional Analysis (as a directed study course with a prof), and the other is doing a...

Hi all, first post :) I have a system of z-propagated nonlinear PDEs that I solve numerically via a pseudo-spectral method which incorporates adaptive step size control using a Runge-Kutta-Fehlberg technique. This approach is fine over short propagation lengths but computation times don't...

Hi all, i have a problem to solve that i want maybe to solve with MATLAB o excel. I have a numerical samples and with linear approsimation i have a function, but now i want to use less samples for example only 20 and i want to find the best set of samples to approsimate in the best way the...

Homework Statement I am working on a problem for my Thermal Physics course. In short, its a numerical problem. I had to go through some Excel calculations and end up with two columns of numbers. One, C/Nk, where C-heat capacity, k-boltzmann constant, N-number of particles and the other is...

Homework Statement See the image: http://postimage.org/image/o19oxb5pj/ You can click on the image to enlarge it.Homework Equations f<=fs=µsN fk=µkNThe Attempt at a Solution Ok, so displacement covered by big block + l= displacement covered by small block, I think. As whole system...

Dear, I need few Resources to get the help for my above topic. The above topic depicts that: one image will be imposed on the other one. and we have to shown it using numerical analysis. of course significant amount of programming effort is here. But I need help regarding resources/articles...

Dear All, I need a few resources to get help with my above topic. The above topic depicts that: one image will be imposed on the other one, and we have to show it using numerical analysis. Of course significant amount of programming effort is required. But, I need help regarding...

If I have a bunch of sorted numbers spanning a large range of magnitudes, is it better to add them up from smallest to largest or from largest to smallest, or something else? Let's say I'm summing an array A, which is sorted from large to small. Which gives a more accurate result: sum1 = 0...

I'm a sophomore physics major and will be choosing classes for next semester in a couple of weeks. I was planning on taking mathematical methods because I've often heard that it makes a big difference going into the upper level classes but unfortunately, it isn't being offered next year. It has...

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 have a very complicated stiff system, which can be expressed as: x^{\prime}(t)=A(x,y)-B(x,y) y^{\prime}(t)=C(x,y)-D(x,y) I decided to solve it with the fixed-point iteration method (http://en.wikipedia.org/wiki/Fixed_point_iteration) but I also have to use adaptive time stepping to...

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} )...

Maybe I missed the numerical methods books in the textbook forum? But I'd like a few suggestions on good texts that are descriptive in implementing numerical algorithms like root-finding, numerical integration, numerical interpolation, etc. I was about to buy Numerical Recipes But I noticed...

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

This is actually a request, I don't know if these are the correct forums for me to post these kinds of things, but yeah. Alright. I intended to study and learn numerical methods with PDEs on my own. And sadly the only thing I can comprehend is the Liebmann method. :cry: And I got so little...

Author: William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery Title: Numerical Recipes in C++: The Art of Scientific Computing Amazon Link: https://www.amazon.com/dp/0521431085/?tag=pfamazon01-20 Prerequisities: Contents:

a+ib=[(3+i)/(5+i)]5 Thanks.

Hi. I'm a math major but this semester I couldn't take any math class except for a stats course. I already took introductory linear algebra and calc III, which were the prereqs for the numerical analysis. However, I'm on academic probation and really need to get stellar grades next semester...

So I'm taking an applied numerical methods course this year, and we are not putting any emphasis on Matlab. Well, we do use it on homeworks and assignments, but he does not teach us more than the very basics (for, while loops, if iterations). The weird thing is that all the math we learn in the...

Hi everyone, I want to know what disciplines must I study to become an effective numerical modeler? As a numerical modeler, I expect to be able to generate numerical solutions to mathematical problems (via programming) at the same time I want to be able to explain all aspects of my...

Hi all I am trying to solve for an integral whose integrand is a derivative that has a change of variable inside of it. ∫ (dz/dx) * cos(θ) dθ between 0 and pi. I have a function for z(x), and also know the relation between of x and θ, but what I don't know is how to evaluate such...

Gauss Legendre numerical intergration The attachment file contain solved example i don't know how he subsitute and why a2=2 done disappear in the answer please expalin in details

All, I have a system of three coupled PDE and I discretized the equations using finite difference method. It results in a block matrix equations as: [A11 A12 A13] [x1] = [f1] [A21 A22 A23] [x2] = [f2] [A31 A32 A33] [x3] = [f3] where, any of Aij is a square matrix. I use...

Homework Statement Here is the problem The Attempt at a Solution I was able to draw the directional field and found which regions had a positive or negative slope. However I don't get what the question means by "Observe that there is a critical value of α in the interval 0 ≤ α ≤ 1 that...

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...

Homework Statement Let f(x) = x^{n} - ax^{n-1},\: and \: set\: g(x) = x^{n} \\ (a) \: Use\, the\, Sensitivity\, Formula\, to\, give\, a\, prediction\, for\, the\, nonzero\, \\ root \, of\,\; f_{\epsilon }(x) = x^{n} -ax^{n-1} + \epsilon x^{n} \, for\,small\,\epsilon.\\ \\ (b) \...

I am using An Introduction to numerical linear algebra by Charles Cullen and I'm not very satisfied with it. Kindly suggest me some alternatives. Also suggest good linear algebra book to clear up basics. finally also suggest any online study materials, lecture notes, videos regarding the...

Hello, I was just wondering if someone would be kind enough to help me with some numerical analysis questions. I am struggling through the course and am completely lost with how to do the methods. I've looked at some youtube videos and such but that doesn't help much either. I need someone to go...

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 Two beetles run across flat sand, starting at the same point. Beetle 1 runs 0.50m due east, then 0.80m at 30° north of due east. Beetle 2 also makes two runs; the first is 1.6m at 40° east of due north. What must be (a) the magnitude and (b) the direction of its second run...

Hello Forum, the numerical aperture NA of a fiber optics is given by the square root of the squared core index minus the squared cladding index. The NA indicates the angular ability to collect light from the outside of the fiber, i.e. the max semi-angle over which light will enter the fiber...

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 Homework Equations Square Packing: V_f = ∏/4(r/R)^2 E=σ/ε The Attempt at a Solution E=10MPa/0.001 = 1x10^4 E_2f=? V_m=? I get stuck here, am I on the right track with this problem? I need some guidance, please!

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...

Homework Statement I have this equation: y = 5(1 - e-x) and I need to find its root. Homework Equations I'm trying to go from Planck's blackbody formula to wien's displacement law by taking the derivative of Planck's blackbody formula with respect to wavelength and then setting it...

Hi all, I have a family of nasty integrals to do, all of the general form \int ^{\infty} _0 db b J_0 (b q)(e^{i\chi(b)}-1) where chi is a complicated real function, typically a sum of products of special functions. (q is a real number.) The only thing that the different functions have...

Hi, I'm a new user of this forum and i wanted to know how i can use calculus and interpolation in my projects. I'm a student in engineering and i usually do home made electronics and computer programming projects, i would like to include calculus to my projects and understand the practical side...

All, As part of my research I came up with a boundary value problem where I need to solve the following system of coupled PDE: 1- a1 * f,xx + a2 * f,yy + a3 * g,xx + a4 * g,yy - a5 * f - a6 * g = 0 2- b1 * f,xx + b2 * f,yy + b3 * g,xx + b4 * g,yy - b5 * f - b6 * g = 0 Where, ai's...

I'm interested in working out an efficient and precise numerical method to find the charge density on a conductor with an axially symmetric shape that is essentially a deformed sphere. (I have in mind something like r(\theta)=\sum \beta_\ell P_\ell(\cos\theta), where P is a Legendre polynomial.)...

Homework Statement a,b\in R, a<b, n\in N\\ h=\frac{b-a}{n} , x_i = a+ih , i=0..n \\ f\in C^1[a,b] we approximate the integral of f in a,b with Q_n(f) = h\left[f(x_1) + f(x_1) + ... + f(x_n)\right] Find the error R_n(f) = \int_a^bf(x)dx - Q_n(f), as function of the first derivative of f...

Homework Statement I have a doubt about how to solve an integral and what numerical method I could use to solve it. Example A = [1,2;2,4] Contour = [0,0,1,1] r = I-mean; integral of the position where the contour is equal zero and obtaining from that positon the value Ai which is...

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...

Hi All, A slight problem I've had with a function defined by a numerical integral. The definition is f[q_,c_,n_]:=NIntegrate[\[Beta]*BesselJ[0,q*\[Beta]]*(E^(I*c*((\[Beta] BesselK[1,\[Beta]] HypergeometricPFQ[{1},{1+n/2,1+n/2},\[Beta]^2/4]+n BesselK[0,\[Beta]]...

suppose an>0, \sumandiverges then what can we say about \sum an/1+nan I think it divergent, but I'm not sure。