Numerical Definition and 775 Threads

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...

How can I speed up some calculations in maple? I have a function f(A)=A*I_0(A)/I_1(A)-c0*log(A/I_1(0))-1 I_0(A)=NInt(exp(A*c1*cos(x)*cos(y)*cos(z)), 0..2*Pi) I_1(A)=NInt(cos(x)*cos(y)*cos(z)*exp(A*c1*cos(x)*cos(y)*cos(z)), 0..2*Pi) c0 and c1 are known constants. I need to solve the...

Hello all, This is my first post... I am trying to make a code to numerically solve a problem, which is a heat conduction problem (temperature) in a moving slab (in y-z plane) with a source term in it: A(dT/dy)=(d2T/dy2 + d2T/dz2) + B dT/dy=0 at y=0, T=given at y=0, boundary...

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...

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?

(a) I found the answer to be: 1/(1-x) = 1 + x + x^2 + x^3 + ... + [x^(n+1)]/(1-x) for x != 1 *Note: "^" precedes a superscript, "!=" means "does not equal" (b) Use part (a) to find a Taylor polynomial of a general (3n)th degree for: f(x) = (1/x)*Integral[(1/(1 + t^3), t, 0, x] *Note...

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...

The data \below gives the list of values for f(x) = e^{0.1x^2} Approximate f(1.25) by using H5 (1.25) and H3 (1.25) wqhere H5 uses nodes x0 =1, x1 =2, x2 = 3. and H3 uses nodes x0=1, x1 = 1.5 Find error bounds for those approximations this questio nand its data table is given in question...

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...

Hi, here's my question...We have to determine whether or not the formulas down there are numerically stable for the cases where x >=0 and x<0. I say that the formulas are stable for x>=0 but not for x<0 because you are subracting numbers that could be close to each other. My problem is that I...

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...