Numerical Definition and 775 Threads

Homework Statement Given that \Omega \subset \mathbb{R}^2 and (x,y) \in [0,1] \times [0,1]. The goal is to find u:(x,y) \in \Omega \longmapsto u(x,y) \in \mathbb{R}. Homework Equations Details: (P1) \left\{ \begin{array}{rlc} -\frac{\partial}{\partial x^2} u(x,y) -...

I have tried searching and have not come up with an answer to this question - but have come close in my own work (i think). Note: I want to solve this numerically, or by some formula. I am trying to solve this problem, save I have function f(x), the equation is not known. Its derivative...

Hi, I studied concept of numerical aperture and f number I learned numerical aperture(N.A) is measure of how much light can be entered into the optical system, its mathematical expression is N.A = nsin\theta_m where n is index of refraction of immersing medium surrounding lens and...

Hi, I need to solve the following simple ODE with both the Euler Forward and Euler Backward numerical methods. I also need to answer for which values of T this can still be calculated: y'(t) = \frac{-1}{2y(t)} y(0) = 2 t \in (0, T] Obviously the analytical solution is y(t) = \sqrt{4 - t} So it...

Homework Statement I am supposed to evaluate the integral using partial fractions. \int \frac{1}{(x+5)^2(x-1)} dx 2. The attempt at a solution So after doing all the work, I get (-1/36)ln|x+5| - (13/6)ln|x+5| + (1/36)ln|x-1| But the answer in the book appears as (-1/36)ln|x+5| -...

Homework Statement Show that if we fit f(x) over [xn,xn+1], with a first-degree polynomial that interpolates f at xn and xn+1, then f(x)=f(xn)+[f(xn+1)-f(xn)](x-xn)/h. Putting that approximation into the relevant equation 1 which is given at relevant equations part derive the approximation...

Homework Statement Consider the equation y0 = Ly; y(0) = 1: **L = lamda** Verify that the solution to this equation is y(t) = e^(Lt). We want to solve this equation numerically to obtain an approximation to y(1). Consider the two following methods to approximate the solution to this...

What are some simple techniques to numerically integrate functions with poles?

Hi everyone, I am writing a simple code using Numerical Recipes (that bible of numerical method) to integrate using trapezoid rule the following integral int_pi/2_inf {sin(x)/x^2} dx I first make variable change y = 1/x to change limit of integration so that now the integral becomes...

hi there, I am a bit stuck can someone help? i have a 5 point grid --_______v1 --_______| --_______| v3-------v0-------v4 --_______| --_______| --_______v2 --_______ used to postion the | (y-axis) the grid is a plus sign. they are seprated by \deltax and \deltay i've worked...

This is a riddle that has proven to be a stumper. At least, the people I have asked... The task is to unravel the meaning of the variables to find numerical answers. Can you do it? Solve for "s", "t", "r", and "u:" *Edit* When Zero is not a solution. *Edit* s * s & = & & s \\...

We've covering numerical integration in one of my classes this semester, however I'm sort of at a loss as to how to deal with error in when using a taylor expansion for numerical integration, and also order of method (Big Oh?) and what exactly it means and was wondering if anyone could explain...

I'm doing some numerical integration using C++ with Visual Studio. Are there any free online libraries where I can find routines to help with this? If there are, what is recommended and would be compatible with VC++? I have looked at the GNU library, but from what I understand this only works on...

Hi, Friends How to numerically do with step function? I mean, this function is very sensitive to the precision. For example, f(x) is a step function. When x is greater than some very small positive number, \delta, the numerical answer is 1, which agrees with the expected value. But when x <...

I am required to solve the following system of ODEs numerically. Could someone suggest an appropriate methodology. These equations are phenomenological equations derived from irreversible thermodynamics. I have to solve for the flux terms given on the L.H.S. The coefficients of differentials on...

I am picking courses for next semester and am torn between a numerical analysis class or one on Fourier series and wavelets. The n.a. course fits my schedule way better but every book and syllabus I have browsed concerning numerical analysis has seemed uninteresting--more like a branch of CS...

Hi, I developed this numerical model where I solve a set of PDEs that allows me to simulate an imaging detector with different parameters, etc. Now, I would like to compare my model with a particular case where experimental data has been obtained. I made a very simple plot to explain what I...

Hi everybody! I kindly request your help in optimizing the numerical integration of the following expression: \xi (r)=\frac{1}{2\pi ^2}\int_{-\infty}^{\infty}f(k)\cdot \sin(k\cdot r)\cdot dk f(k) vanishes outside the boundaries k=0 and k=2; I have got k and f(k) as float arrays, so we...

I've got the following ODE: K*w''''+c*w = q I can solve this with DSolve (from Matlab), but how can I solve this in a numerical way? Thanks!

OK...this is a really trivial question, but I hope someone can help me here. I am working on building a segway-style robot that balances on two wheels, but I am having some difficulties integrating the data I receive from my gyro sensor. The sensor gives me the angular velocity, and I know...

Here is an integral (similar in form to the one) I want to evaluate: $$ \int_{r_1}^{r_2} R \left\{ \int_{x_1}^{x_2} Y(x,R)\, dx \right\}^2\,dR $$ This is my approach - please correct me because I don't think it's right: I treat R as a constant and evaluate the inner integral over some vector of...

Homework Statement There is a fluid flowing over a hot plate. We non-dimensionalized the problem from three partial diff eq's to two ode's. I am modeling I have two coupled differential equations that are a system of initial value problems. I am supposed to numerically integrate the two...

I'm having trouble with a sample exam question. I don't really understand the question, don't know what section of the book it relates to, and don't have any idea on how to solve it. I might be in trouble :) Can anyone provide any suggestions or guidance on how I might go about solving this...

I am trying to model a packed bed distillation column for a binary liquid in Python. Unfortunately, when I set up my system, I end up with a system of coupled non-linear first order ODEs with boundary conditions at opposite ends (feed conditions and exit conditions), and I do not know how to...

Hello. I have a fluid in a rectangular basin, driven by stokes drift at the southern wall. The problem is formulated as follows: \begin{align*} -U_y+V_x &= g_1(x,y) \\ U_x+V_y &= g_2(x,y) \\ U(x=0)=U(x=M)&=V(y=0)=V(y=N) = 0 \end{align*} Here, g_1 and g_2 are known functions of the horisontal...

Homework Statement I am given a table of data derived from experiment. A force (F) is applied to a spring and the extension (x) is measured and recorded. An additional column of data for the derivative (dF/dx) is also provided. Here is the data: x(m) F(kN) df/dx (kN/m) 0.0...

hey folks, been a long time since i been here, stranded on a tropical island for a few years.. nice to be back to the business. I have a problem with some " rhetoric" i was reading today in one of the old posts. Seems to me that you all seem to think that .999 followed by about 1billion...

Hi, I have a set of over 1000 field measurements as a function of Z. I want to multiply them by COS(Z) and integrate with respect to Z. I have tried using the quadl function but to no avail. Is what I want to do possible in Matlab (ie. is there a built in function for this) and if so...

here is a simplified version of my working equtions y''' = \frac{(y'' y+y' y) y + y'y''}{y' + y''} and 3 related boundary conditions, is there some hints to solve such equation numerically? ThX

Suppose for some specific problem (symmetric potential well) the Schroedinger equation is expected to give certain discrete bound states and corresponding eigenfunctions. Now I am trying to obtain the eigenfunctions by numerically solving the equation and plotting the solutions by randomly...

How good do I have to be with numbers in upper division math( esp. linear algebra and probability)? I have pretty good spatial skills, logic and algebra( I can solve differential equations quickly with little error). I got mostly A's in lower division math and, if it counts for anything, physics...

Hello I have the following question in numerical integration in higher dimension. Any help/suggestion would be welcome. The integral is ( I am using maple notation ): int( int( int( int( int( int( f(x,y,z), z=-infinity..w), w=-infinity..infinity)...

Hi, does anyone know what sort of methods I could use to test the accuracy of the numerical solution of the integral equation? Many thanks

Hello everyone :), I'm sure someone will have no problem helping me with this. How do I figure out large powered numerical values without using a calculator. Kept getting questions involving 2^2007 and others. How would I be able to figure out these values without using a calculator or a...

So I'm trying to teach myself physics and I've been doing problems in books. I started with griffiths qm but it has no answers. I became incredibly frustrated because there was no way to check if I was doing the work correctly, and my math skills weren't good. Now I'm working through Mary Boas'...

Hello, I have a math problem that I think I've worked out properly, but I'm not entirely sure. The explanation is a bit lengthy, but I don't want to miss anything that might be pertinent. Essentially, I have a force equation F(t) that describes the acceleration of a body in two dimensions...

Hi to all, I've been around this forum for some time now, but this is the first time I actually registered in need to ask you for some help to crack this. I've seen some great minds who surely could give me some lights. Thanks to all :) Homework Statement So, um trying to create a numerical...

Hello. I've recently been using a few different numerical integration methods to solve a number of different problems, and as I looked into the integration algorithms, I realized that I don't understand them as well as I thought I did. I created a simple Excel workbook that calculates the...

The trapezoidal rule for numerical integration is based on the idea that when we partition our larger interval into subintervals, we can approximate the area over each subinterval by calculating the area of the trapezoid formed by connecting the value of the function at the left and right...

Homework Statement Im having problem of even starting this question: "Determine the positive integer N = abcdef such that 6N = defabc" any ideas? Homework Equations The Attempt at a Solution

While working out a problem I got a result which gave rise to this doubt regarding value of action functional. Suppose I start from an action, obtain the equation of motion and when I try to check if that solution gives a finite value of action, I get, surprisingly, vanishing value. The actual...

I want to make a simple program for numerical solving of elastomechanic problems. The basic task it should perform is the calculation of deformation of a two dimensional homogeneous, isotropic body in the field of gravity and/or deformation under external force. The basic idea for each time...

What do you think about Gravitational wave physics and numerical relativity ? Will it expand much in future? Now few universities are giving research facilities on these two. Why ? But i really like these two.

There isn't an applied mathematics thread so i'll post this here. I'm an undergraduate and I have a presentation for my numerical methods/matlab class . I'm looking for examples of 1)Integrals which are easier/faster to integrate numerically than do evaluate using their antiderivatives...

for each of these careers: engineer, physicist, mathematician, how much numerical analysis is necessary? is just learning mathematica sufficient? or do you need at least a full class in numerical analysis?

give a numerical method of order bigger or equals 2 for the numerical solution of: y'''(x)+2xy'(x)+e^(y(x))=cos(x) in the interval: [0,1] with boundary conditions: y(0)=1,y(1)=2,y'(0)=0 Attempt at solving: well I thought of difference equation...

Hi guys, I'm finishing up a term project in a numerical analysis course, and one of the last things left that I need to do is provide a brief survey of the methods used by modern researchers to solve the 2-D wave equation initial boundary value problem. My group solved this equation for an...

Is there a numerical method for finding solutions to 2nd order non-homogeneous differential equations? Thanks.

Homework Statement Approximate the solution of: \frac{\partial^{2}u }{{\partial r^{2} }} + \frac{1}{r}\frac{\partial u}{\partial r} + \frac{1}{r^{2}}\frac{\partial^{2}u}{\partial \theta^{2}} = 0, 1<r<3, 0<\theta<\pi, u(1,\theta) = 1-\cos(\theta),u(2,\theta)=u(r,0)=0 u(r,\pi)=4-2r...

Hi. Can anyone tell me where to find information on how to evalutate a principal value integral numerically? When I say principal value, I mean an integral where a certain point is excluded from the domain of integration. In my case, the integrand is singular in this point.