Numerical Definition and 775 Threads

Homework Statement Solve the inhomogenous partial differential equation \frac{∂^{2}u}{∂t^{2}}-\frac{∂^{2}u}{∂x^{2}}=-6u^{5}+(8+4ε)u^3-(2+4ε)u by using the NDSolve function in Mathematica for the interval [0,10] x [-5,5]. Homework Equations Initial conditions: u(0,x)= tanh(x)...

Hello all, Suppose I have a simple 1-D signal and I want to compute the hessian. In that case, it should generalise for second derivative for normal scalar functions. So, I observe the signal as v = [x_1, x_2, x_3, x_4...]. Then, numerically the hessian is given as (assuming I am only...

Homework Statement Use a Taylor Polynomial about pi/4 to approximate cos(42){degrees} to an accuracy of 10^-6. *To get an accuracy of 10^-6, use the error term to determine an nth Taylor Polynomial to use. Homework Equations x = 45 or pi/4, x0 = 42 or 7pi/30 cos(x) = Pn(x) + Rn(x)...

Hi, I have to use a wide 5 point stencil to solve a problem to fourth order accuracy. In particular, the one I'm using is: u'' = -f(x + 2h) + 16f(x + h) - 30f(x) + 16f(x - h) - f(x - 2h) / 12h2 or when discretized u'' = -Uj-2 + 16Uj-1 -30Uj + 16Uj+1 -Uj+2 / 12h2 In addition to...

Okay, I'm in a bit of a pickle here. Got the exam on thursday and (surprise) I am utterly clueless. I cannot grasp a lot of concepts, but here's some I'd like to at least get an idea of: Factorization method. I only scrapped that it is a special case of Gauss' Exclusion method, that you take a...

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 Hi, I have to do a simulation of two non linear dynamical equations which represent a electromechanical system. (An inverted pendulum attached to a cart moving over a rail). I am going to simulate the response via numerical methods programmed in LV. (I am trying firts with a...

Hi guys, I need to simulate wave propagation for a nonlinear dispersive wave PDE and since I can't find proper resources for handling nonlinear PDEs numerically, I would appreciate any help and clues. the PDE is in the form of utt-(au+bu2+cu3+duxx)xx=0 Romik Ps: BC: Clamped at both ends IC...

Hi, I have a question about resolution as defined by rayleigh's equation r = 0.61 x lambda/numerical aperture The maximum half angle of acceptance of a lens is 90 degrees and the sine of this is 1. At this point the only thing that can increase the value of the denominator in the equation...

I am currently doing my bachelors in Mechanical engineering engineering and planning to pursue physics after completion. I have to choose an elective the coming semester. One of the electives offered is 'Numerical Methods for Engineers' and the modules covered include Error in numerical...

I would like to find a FORTRAN subroutine or a good way to minimize function numerically.So basically my function has 20 variables and I am able to provide analytic form of the first and the second derivative of the function. Basically what I want is: have the form of the function of 20...

Sorry, but this is the only subject I could not pass even if I gave it my all every day and night of the semester. And I will still surely fail this subject, but as a last resort I will try to post my problem here, hoping to get solution and maybe an explanation. Sorry if some of the phrasing...

Sorry, but this is the only subject I could not pass even if I gave it my all every day and night of the semester. And I will still surely fail this subject, but as a last resort I will try to post my problem here, hoping to get solution and maybe an explanation. Sorry if some of the phrasing...

how does \frac{5700}{\sqrt{15,300}} turn into \frac{570}{\sqrt{153}} ??

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...

Dear Forum : I hung up with a integration http://ppt.cc/mIpV Can it be deduced to a simpler form? The distribution of σ(E) is http://ppt.cc/-5Z5 The estimation width of x is 10MeV , height is 200mb. The distribution of dE/dx is http://ppt.cc/vcVU Is there a way to do some simple...

Hi! I have written two codes in matlab,to implement the Jacobi and Gauss Seidel method.Both of the programs should stop either if the number of iterations surpass the maximum number of iterations MAXIT or if one of these conditions/or both of them: \left \| x_{k}-x_{k-1} \right \|_{2}<ε , \left...

hello i just copied the Numerical Code for the NLS equation which is the following: %---specify input parameters clear all; distance=input('enter fiber length(in units of L_D)='); beta2=input(' dispersion: 1 for normal, -1 for anomalous'); N=input('Nonlinear parameter N=')...

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...

Hey! I am looking at an exercise in Numerical Analysis and I got stuck. Why do we have a huge error when we substact two almost equal numbers?

I need to solve the following system of equations for n=0,1,2 subject to the given initial and boundary conditions. Is it possible to solve the system numerically. If yes, please give me some idea which scheme I should use for better accuracy and how should I proceed. The coupled boundary...

can anyone direct me to a website that gives adequate treatment of the numerical solution of partial differential equations, especially pertaining to problems which involve the use of the Crank-Nicolsen procedure?

Hey all, First time posting on here hope this all goes well! I just worked through a problem on dielectric slab waveguides with core and cladding and it was pretty straight forward finding critical angle, critical angle compliment, number of modes, numerical aperture, maximum acceptance angle...

Homework Statement Numerically determine the period of oscillations for a harmonic oscillator using the Euler-Richardson algorithm. The equation of motion of the harmonic oscillator is described by the following: \frac{d^{2}}{dt^{2}} = - \omega^{2}_{0}x The initial conditions are x(t=0)=1...

Well I think this is really cool, numerical differentiation of real analytic functions by stepping out of the reals: Complex Step Differentiation | Cleve's Corner Even funnier is John D'errico's comment (my amusement is mainly due to the idea that a fourth order finite differences scheme with...

Hi, I'm trying to solve the flow profile inside an inhomogeneous porous material between two parallel moving plates (essentially Couette flow with a deviation), and I model my system by the following equations: \nabla^2 \mathbf{u} = p(x,y,z) \mathbf{u}\\ \nabla \cdot \mathbf{u} = 0...

Are there any uses of numerical analysis in industry (outside of financial firms)? I get the impression that a lot of industrial software has already been written and standardized so you don't really have people coming up with innovative ways to e.g. numerically solve PDEs so much as using...

I am looking for book recommendations that go over and has numerical code for solving PDEs. The book can be based on Matlab or Python. I already know how to numerical solve PDEs so I am looking for a more advanced book not a basic one.

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...

I have a function Z = f(P,T) and would like to calculate the partial differentials \left ( \frac{\partial Z}{\partial P} \right )_T and \left ( \frac{\partial Z}{\partial T} \right )_P at values of P and T. The function Z is compressibility factor (Lee and Kessler equation of state), P...

Homework Statement Show f(x)=(x−2)sinxln(x+2) has f'(x)=0 somewhere on [-1,3] The Attempt at a Solution I tried using Rolle's theorem, but f(-1)≠f(3). Then I tried the mean value theorem, but didn't get 0 either.

Homework Statement Consider a solid sphere of radius r and mass m which has a charge q distributed uniformly over its volume. The sphere is rotated about the diameter with an angular speed ω. Show that magnetic moment μ and the angular momentum l of the sphere is related as, μ=ql/2m Homework...

Can anyone tell me for which problems you should use these numerical methods: - finite difference method - finite element method - boundary element method - method of moments For example I read that finite element method is often used for car crash simulations, and that it gives very...

Homework Statement In my book, for a class on numerical analysis, we are given the definition: "Suppose {β_{n}}from n=1 → ∞ is a sequence known to converge to zero, and \alpha_{n} converges to a number \alpha. If a positive constant K exists with |\alpha_{n} - \alpha|≤K|β_{n}|, for large...

Homework Statement An optical system consists of a thin lens in air with f = 100 mm. An aperture stop with a diameter of 20 mm is placed 25 mm to the right of the lens. Calculate the numerical aperture of the system. (Hint: Find the size of the entrance pupil.) What would be the numerical...

Hello Everyone, Actually i would like to have a clear Explanation about Runge Phenomenon. Could you help me Please.

I took a CFD class last semester (had to leave school though due to personal garbage). I am making a come back this fall and as some extra credit I am trying to numerically solve the unsteady laminar flow equation in a pipe. The equation is \dot{U} + U'' + K = 0 where dots denote the time...

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?

Hello guys, First of all this is not a homework. I am preparing for my exams and this question was asked in my previous exams so I tried to solve this question myself, I have tried to solve this numerical by myself, but couldn't get the answers right. So, I am posting this question here, in...

I am doing a little research project into numerical methods of solving ODEs where I do 1 half of learning about the basics of numerical methods and then look at a particular method (Linear multistep) and then the second half is looking at a particular example, applying what I've learned and...

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...

What is the most general method of approximating arbitrary systems of ODEs of 4 variables(x,y,z,t) that fit these conditions? The conditions that are assumed true of the ODEs are: 1) that I require differentials to be explicitly defined (but they can be defined in terms of other...

I have established existence and uniqueness of solutions to a nonlinear elliptic system of PDE's and would like to see how the solutions look like numerically. I have some programming background on MatLab and C++. I also understand basic ODE numerical schemes. But I am not so sure, if I need to...

I need to choose one more math class to reach a full-time status for next fall. So far I am already taking Classical Mech I from Physics Dept, Analysis I and PDE from Math Dept. I hear Analysis is already time-consuming hard class and I guess PDE isn't easy either, so I am considering to...

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...

Hello, I have been encountered an integral equation that I need to solve\evaluate numericly and I didn't find anything like it in my search yet. The equation: \frac{d^2 F(t)}{dt^2}=const*\int_{t'}\frac{sin(F(t)-F(t'))}{(t-t')^{2k}}dt' If it helps there is a specific case, when K=1...

I'm trying to create a java application that models the path of a double pendulum. To do so I have been attempting to use Lagrangian Mechanics to find the equation's of motion for the system. The problem is that I have never seen a set of equations like the one yielded by this method and need...

so I have this homework as I said and marks will be added on my total, so if anyone could help you will be a lifesaver, you don't have to answer the whole thing , just help me with the part you know, here it is : A function g (x) is called Lipschitz function on the interval [a,b] if there...

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...