Numerical Definition and 701 Threads

Any recommendations? The books I have are very outdated. Extremely important to me are: - worked examples #1 criteria. Need that bridge between theory and implementation. - not overly heavy on theory (don't want to hire a PhD to explain it). I have an MS Engineering level education...

Hi all, I am having trouble numerically integrating a function using Maple 10. Here is a bit of background on the problem: This problem is asking for two plots, one of the velocity of a sounding rocket with respect to time, and the other being the height of the sounding rocket with...

On the piece of paper handed out in class please write a number between 0 and 100. The winner is the one who comes closest to 2/3rds of the average of numbers written by the students of the class. Question: What number should you write?

Consider the fixed point iteration formula: *x_(n+1) = (2/3)[(x_n)^3 - 1] - 3(x_n)^2 + 4x_n = g(x) *Note: "_" precedes a subscript and "^" precedes a superscript (a) Find an interval in which every starting point x_0 will definitely converge to alpha = 1. (b) Show that the order of the...

I have a system of spatial ODEs to solve... Actually a DAE system, but here's the issue: The equations are vaild over a specific domain, x = 0..L The equations are only bound at one point (thier "initial point") but at either 0 or L f1(0)=0 f2(0)=100 f3(L)=0 f4(L)=100 (also an...

Has anybody got the source code in C++ for cubic spline interpolation?Need for my lab..

given five points of a function one can approximate the derivate of the function at some point. The standard five point formula is Derive an O(h^4) five point formula to approximate f'(x0) that uses f(x_{0}-h), f(x_{0}), f(x_{0} +h),f(x_{0} +2h),f(x_{0} +3h) . (Hint:Consider the...

I have some problems which says show that (i) \sum_{n=1}^\infty \frac{1}{n^4} = \frac{\pi^4}{90} and (ii) \sum_{n=1}^\infty \frac{(-1)^{n-1}}{n^2} = \frac{\pi^2}{12} And another one which says, show that for 0<x<\pi sin x + \frac{sin 3x}{3} + \frac{sin 5x}{5} + ... = \frac{\pi}{4} The...

Imagine: I want to compute numerically a POTENTIAL STEADY and INCOMPRESSIBLE flow over an airfoil. The set up of the problem is: \nabla^2\phi=0 \nabla\phi \cdot \overline{n}\big)_{x=surface}=0 no normal velocity component on the airfoil surface. \nabla \phi=\overline{U_\infty} as...

Got this problem and we've been given a program which can solve for x, for the equation: Ax = b Where A = \left( \begin{array}{rrrrrr} b & c & 0 & 0 & \cdots & 0 \\ a & b & c & 0 & \cdots & 0\\ 0 & \ddots & \ddots & \ddots & & \vdots \\ \vdots & & \ddots & \ddots & \ddots & 0 \\ \vdots & & &...

The following 2 page example illustrates the use of the Newton-Raphson technique for solving for roots of functions. Examples included: 1. Function in a single variable 2. System of non-linear equations

PROBLEM:the current at the terminals of a certain current source is measured with an ammeter having an internal resistance R_i=10 ohms and is found to be 11.988 mA ;adding a 1.2 kilo -ohms resistance between the source terminals causes the ammeter reading to drop to 11.889 mA.Find i_s and R_s...

Find intervals containing solutions to 4x^2 - e^x = 0 well someone suggested i sketch the graphs of 4x^2 and 2^x but I am not sure on how to go past that point... All i have to do is find the intervals so do the intersection point(s) of these two functions indicate the intervals where the...

Find the intervals containing solutions to the following equation 4x^2 - e^x = 0 I haven o clue on where to start really? WOuldi expand e^x using taylor series? i mean one could do this x - 2ln x = ln 4 so then would i do log expansion by taylor series? Or would i use bisection...

Not a hard question really.. Using 3 - digit arithmetic calculcate 4/5 + 1/3 and compute the relative error 4/5 + 1/3 = 17/15 chopping 4/5 = 0.800 and 1/3 = 0.333 0.800 + 0.333 = 1.133 (chop) 1.13 im assuming that after this point there is no chopping relative error aboslute value of...

Hello there! yet another proof, that i need help on I am supposed to prove that the following statement holds for the secant method dk+1/ek -> -1 for k->Infinity where dk+1 is the next change and ek is the error. I have this idea, but i want to hear whether its a valid proof. i use...

Like any loan, the government accrues interest that compounds over time on the amount it owes. If the annual interest rate is r, then the number of years it takes for the amount of money owed to increase by a factor of x is Y=1/r ln(x) where ln is the natural logarithm. The average...

Here are my questions: "Evaluating the summation as i goes from 1 to n of a sub i in floating point arithemetic may lead to an arbirarily large error. If however, all summands a sub i are of the same sign, then this relative error is bounded. Derive a crude bound for this error, disregarding...

Could somebody who knows well the method of numerical solutions of system of nonlinear algebraic equations nonlinear algebraic equations recommand a global convergence methods? thank you very much!

Any body use or know of any good numerical analysis packages in C/C++. something like LAPACK. and are they easy to use.

hello all I have been researching into numerical analysis, differential equations in particular, I underdstand how the Runge kutta methods work geometrically but I don't quit understand what is the idea behind Adam moultons method And Adam Bashforth method, Is there a graphical way of...

Im supposed to solve integral 10 to +infinity ((sin(1/x)/(1+x^3))dx with error precision of e=0.5*10^-4. Can someone please give me detailed explenation of solving this. (Supposedly by Simpson but i get lost in the way. P.S. sorry for bad spelling and lack of proper formula notions.

Im supposed to solve integral 10 to +infinity ((sin(1/x)/(1+x^3))dx with error precision of e=0.5*10^-4. Can someone please give me detailed explenation of solving this. (Supposedly by Simpson but i get lost in the way. P.S. sorry for bad spelling and lack of proper formula notions.

Hi, Does anyone know a reason why \int_{-\infty}^{\infty}\cosh(x)^{-n}dx (n>0) can be evaluated analytically when n = 1,2,3,..., but only numerically when n is non-integer. I don't know if there is a "reason", but I'm using this result in a Quantum Mechanics project and it would be cool if I...

:cry: I have an essay to write on modern trends in the numerical solution of differential equations. Most of the journals I've been reading are quite hectic and higher grade for me. ^^, Neway, if anybody knows of any good articlkes that i could read that would be great. Do ppl still use...

No numerical sort in python ? I was really surprised to see that python can't do such an elementary operation! I am trying to do a numerical sort in python on an array. I am using python for windows (DOS). In perl you can simply write sort{$a<=>$b}@a and this will sort it according to the...

Hello, I am given the method: y_(n+1) = y_n + h f(t_n + w h, (1-w)y_n + w y_(n+1). I am to determine the region of absolute stability; I am also to determine for which w in [0, 1] is the method A(a) stable, i.e., the region of absolute stability contains a sector about the negative...

Suppose we have y'' = f(t, y); y(a) = y0; y'(a) = y0' Note all derivatives are with respect to t. Let u = y', then u' = y'' 1. u' = f(t, y), u(a) = y'(a) 2. y' = u, y(a) = y0 Question 1: For y' = u, should I think of this as dy/du = u? Otherwise, I don't see how to solve 2 because...

2+2=4 4+4=8 142+468=621 3762+8271=? driving me crazy

Hello there, I've not been here in a while, but I'm stuck doing this integration and wondered if some of you kind people would help :smile: \int_0^\infty \frac{1} {(1+x)\sqrt{x}} dx (appologies for the lack of spacing in there...) anyways, I know that when x tends to infinity, the...

Numerical Methods Help! I have been trying to understand the differences between Finite-Difference Time-Domain (FDTD), Finite Volume, and the Finite Elements methods of solving Maxwell's equations numerically. I have used the FDTD method for solving Maxwells Equations. I did this without...

I need help with this numerical simpsons rule problem x y 16 -5 17 1 18 3 19 -3 20 -5 21 6 22 -8 Use the table to estimate the value of the integral y from the interval 16 to 22 the problem i am having is how many subdivision to make and how to...

I have a dobut,can a complex integral be evaluated by using numerical analisis?..for example the integral LnR(s)/R(s) where R(s) is Riemann Zeta function with the limits (c+i8,c-i8) i would use the change of variable s=c+iu so the integral becomes a real integral with the limit (-8,8) now how...

Hello, I have to do a proof and am having trouble starting. The proof is to show how you could use Cholesky decomposition to determine a set of A-orthogonal directions. Cholesky decom. means I can write the symmetric positive definite matrix as A = GG' The textbook gives a way...

e^{-2 \lambda}(2r \lambda_r -1) + 1 = 8 \pi r^2G_\Phi(r,\mu) e^{-2 \lambda}(2r \mu_r +1) - 1 = 8 \pi r^2H_\Phi(r,\mu) where G_\Phi(r,\mu) = \frac{2\pi}{r^2}\int_{1}^{\infty}\int_{0}^{r^2(\epsilon^2-1)} \Phi(e^{\mu(r)\epsilon,L}) \frac{\epsilon}{\sqrt{\epsilon^2-1-L/r^2}}dL...

I'm need to use Microsoft Excel as a numerical analysis tool for classical mechanics physics problems. Yes, I know there are dozens or hundreds of other tools that would be more powerful, but I (and my students) are required to see what they can do with Excel. The Class: Analytical...

I feel so embarrased asking this question, but this is the place to get answers. I have a 2nd order ODE with a forcing function that needs to be manipulated and put into a matrix for a numerical method solution, ie Matlab. My question is: Is the matrix composed of a particular solution in the...

I've just got my final year project assigned. It has to do with a numerical simulation of a Ram Accelerator device. Well, apart of having doubts, which I will post just here proximately, I would want to know some website to learn more about that type of device. Apart of Google sites...

Hi Everybody, Does anybody know how to solve, analytically or numerically, the following differential equation : \frac{d^2\Phi}{dx^2}-a.Sinh(\frac{\Phi}{U_{th}})=-b.Exp(-(\frac{x-x_{m}}{\sigma})^2}) The unknown function is \Phi. a and b are some strictly positive constants. q\Phi is...

I am performing the numerical integration of finding the area of 1/x dx from 0 to 2... using Simpson's rule of n = 6. What will I do in this problem like this since 0 to be evaluated in the f(x) = 1/x is undefined?

I'll be taking Numerical Analysis in the fall and I honestly have no idea what it's about. Can anyone tell me what the main topics in Numerical Analysis Are? Thanks.

i found this in my wandering in google: http://pdg.cecm.sfu.ca/~warp/papers/essay/essay.html can someone explain to me this approach of quantum gravity in simple terms? i think it has to do with simulations of quantum gravity at the Planck level, am i correct?

I understand that one can use numerical methods to solve a derivative or integral that can't be solved analytically. What are some simple examples of physics Diff Eqs and/or Integrals that can only be solved using numerical methods?

Forum, I'm seeking for a good textbook on numerical celestial mechanics. My current level of proficiency is: 1- understanding of classical mechanics is at the level of Goldstein's textbook 2- understanding of numerical analysis is at the level that I can easily pick up an algorithm from the...

Best numerical technique? I've recently used Simpson's (1/3) rule for the numerical solution of the 'intersecting cylinders' problem. I've found that it isn't too accurate no matter how many intervals I take (I have even taken 1000,000 intervals!), but still end up with some error. I'll...

I have been doing a simulation of Blasius equation: F'''+FF''/2=0 with F(eta) where eta is a similarity variable eta=(y-1)/(x^(1/2)) F'(0)=1 u(y=1,x<<1)=1 F(0)=0 v(y=1,x<<1)=0 F'(infinite)=0 u(y=infinite, x<<1)=0 You...

I've got a horrible system of 8 coupled differential equations: \frac{\partial}{\partial t} N_0=-R_{0,2}N_0Y_1+\sum_{j=1}^5W_{j,0}N_j-C_{0,1}^{4,2}N_0N_4 \frac{\partial}{\partial t} N_1=-R_{1,3}N_1Y_1-W_{1,0}N_1+W_{2,1}N_2+W_{4,1}N_4+C_{0,1}^{4,2}N_0N_4 \frac{\partial}{\partial...

I'm writing a vehicle physics engine and am using an RK4 integrator which I wrote. But I am having huge problems with angular motion. Long story short I thing it might be to do with the fact that I'm integrating from accelerations. So I'm re-writing the integrator using momentum. However I'm...

How do mathematicians figure out the numerical values of sines and cosines? I can figure out how to evaluate sin(pi/12), sin(pi/24), sin(pi/48), etc, using sin(pi/6) and half angle formulas. How would I find sin(pi/5), for example? Is there any way other than infinite sums to express the...

For those of you familiar with numerical modelling of various phenomena, you will know about work like the various discretisation schemes, stability/gradient limiters for high order schemes and so on. The most broad sweeping improvement to the field of numerical modelling would ultimately be...