Numerical Definition and 775 Threads

I'm looking to do numerical evaluation of a system of differential equations and would like to use the RK4 method however I'm having a problem as my differential equations are respect to different variables and I don't know how to adapt RK4 to allow for that. The general form of the equations of...

Hi all, I am trying to construct a numerical solution to the following linear harmonic problem posed in a wedge of interior angle 0<\alpha<pi/2 \bigtriangledown^2\phi(r,\theta), \ r>0, \ -\alpha<\theta<0 \bigtriangledown\phi\cdot\mathbf{n}=0, r>0,\ \theta=-\alpha...

Would anyone please suggest the best numerical method for integrating complicated integrands and singular functions? I find that Gauss quadratures are suggested by many references but I can't find a method to obtain the abscissas and weights for a general function.

I am trying to solve the potential barrier problem numerically in Mathematica I am giving the following command but it is showing error which i could not figure out a = 2; s = NDSolve[{y1''[x] + k1*y1[x] == 0, y2''[x] + k2*y2[x] == 0, y3''[x] + k1*y3[x] == 0}, {y1[0] == y2[0], y2[a] ==...

Help! Numerical integration in matlab So (assuming the period in a damped harmonic oscillator is constant, because it is right?) I have been asked to find T= 2* (integral from x1 to x2 of(1/v_num)dx) where x1 and x2 are two consecutive extrema (?? not sure what he means with this, i supossed...

Hi I have two general questions regarding a lens and its numerical aperture: 1) From this picture http://en.wikipedia.org/wiki/File:Numerical_aperture_for_a_lens.svg (from the Wiki-article http://en.wikipedia.org/wiki/Numerical_aperture) it seems to me that there is a propotionality between...

Hi guys, I'm currently in computer science program and I have an urgent feeling that I need better exposure to math. I have taken Discrete Math, Calculus i, ii, iii and I've independently studied linear algebra. I guess my concern is lack of differential equations and numerical methods. In...

Hey guys, I'm currently in a 2nd year Honors Physics program & I need to decide within the next ~2 weeks which of these two classes to take. Either Linear algebra II or Numerical Analysis. Heres are course descriptions as given on my Universities website Linear Algebra II Vector space...

This is not so much of a homework problem but a practice problem for our final. Any advice or insight on how to approach this problem would be incredibly helpful! (Btw, I don't expect anyone to solve this for me, just want to make that clear! ) Prove that...

I'm working on a little project that involve some mechanical modeling. So, I wrote a little c program to do some numerical differentiation and integration. I'm using a slight twist on the central difference algorithm for the differentiation and a standard trapezoid algorithm for the...

any suggestions for a nice book regarding numerical methods in c?

Hallo, \Gamma(t) is a function that i can know only at dicrete points and appears in this integral: \int\Gamma(t) * tan (\Gamma(t)*t + \varphi) My question is now, which could be the best interpolation of \Gamma(t) that would allopw an exact integration? Thank you very much in advance

Hi! I'm trying to implement an implicit scheme for the continuity equation. The scheme is the following: http://img28.imageshack.us/img28/3196/screenshot20111130at003.png With \rho being the density, \alpha is a weighing constant. d is a parameter that relates the grid spacing to the...

I have a system of non-linear coupled PDEs, taken from a paper from the 1980s which I would like to numerically solve. I would prefer not to use a numerical Package like MatLab or Mathematica, though I will if I need to. I would like to know if anyone knows how to solve non-linear coupled...

Using ΔX=XH-XL as one of the convergence criteria in regula falsi may lead to infinite looping, e.g. f(x)=0.5x-2ln(x), with a bracket [7,10]. A better choice is to use the approximation error ΔX=|ΔXR|, i.e, the difference between the current estimate and the previous estimate of the root...

Hi! I'm implementing a scheme to solve the following equation \frac{\partial \psi}{\partial t}=-c_{s} \cdot \frac{\partial \phi}{\partial x} \frac{\partial \phi}{\partial t}=-c_{s} \cdot \frac{\partial \psi}{\partial x} c_{s} is just the isothermal velocity of sound. The equations are for a...

Hello to all! I was wondering if anyone would help clarify a couple of things please. I have two data sets. The first data set has two grouped variables. The second data set has eight independent variables (let's call them learning methods) My understanding is that the aim of this...

Could someone please direct me to a good book/article that describes how to use a coarse and fine spatial mesh with the numerical method of characteristics? Thank you. Kate

Hello guys, I have some experience with numerical methods and simulating various physical phenomena. Recently i was searching for a new research problem where i can do numerical studies and which can lead to a research paper. Do you guys have any suggestions?

I have doubt in MATLAB How to integrate exp(x)*erfc(x) ? in MATLAB The warning msg it is displaying is : EXPLICIT integral could not be found

Hi I don't have idea about solving it, If anyone can give me a descriptive answer or solve it for me, it'll be appreciable The flywheel of a prototype car engine is under test. The angular position θ of the flywheel is given by θ = (3.0rad/s3)t3 and the diameter of the flywheel is 36cm...

A worker pushes 25Kg crate a distance of 5m along a level floor at constant velocity by pushing horizontally on it. The coefficient of kinetic frication between the crate and the floor is 0.23...

Homework Statement Consider the second order wave equation u_{tt} = 4u_{xx} There are initial and boundary conditions attached, but I'm less concerned with those for the moment. I think I can figure those out if I can figure out where to get started. Rewrite this as a system of first order...

Hi everyone, I am finishing my second year of masters in France on theoretical physics and I am really really motivated in pursuing into a PhD. The topics that interest me the most are lattice QCD and numerical relativity (I want to focus on numerical methods). Also, I would like to work on one...

Homework Statement Some tourists return to the same country several times in the same year. In 2000, it was noted that 80% of tourists made a single trip to the country, 15% came twice, and 5% came at least three times. How many individual tourists visited Italy in 2000. (Table shows...

Hi all, I need to use some numerical simulation programs. The source code is provided in Fortran 90 but I'm not able to compile it. I'm using G95 complier on WinXP, and the code are avilable at the following address: http://www2.fz-juelich.de/jsc/splim/ Could you provide any step by...

This isn't so much of a homework problem as a general question that will help me with my homework. I am supposed to prove that a given function is uniformly continuous on an open interval (a,b). Since for any continuous function on a closed interval is uniformly continuous, I am curious...

ok, I'm not completely sure which section this goes into, but since I'm using this to solve a PDE ima going to put it in here, I need to integrate w(x,y,z)*V(x,y,z) over a cylindrical domain, it would be fairly simple if V had a "formula" describing the function, but i only have V as a number...

Homework Statement An object of mass m falls from rest at a point near the Earth's surface. If the air resistance is proportional to the velocity v^2, the differential equation for the velocity as a function of time is given by m*dv/dt = mg - cv^2 For the given paraments g = 9.81 m/s^2. m...

Hi, For a small problem I'm working on in quantum field theory, I have to numerically evaluate the integral \int_{-\infty}^{t}du e^{i\omega u}erf\left(\frac{u}{\sqrt{2}\sigma}\right) where erf(z) is the error function. Now, I have to replace -\infty by some large negative number, so...

Hi guys, I am looking to integrate the attached equation using C++. I was wondering if you could tell me what type of equation it is, and if you could recommend an algorithm to use to solve this (and why)? I need to use this for 100's of points (m,n) on a grid so a fastish algorithm...

Please, I am new in MATLAB and need some help as to whether MATLAB can perform this integration, and how to go about it. I have tried 'quad', 'quad8', 'trapz' and even a sum approach but it returns either a not-a-number answer or mtimes error or mrdivide error message. What I want to do is this...

Homework Statement Assume the spring force of a bowstring acting on an arrow does not follow Hooke’s Law because the bow’s material becomes more rigid as it is drawn back. The string’s force as a function of the drawback distance in meters is: F(x) = -k1x -k2x|x| where positive x is along...

Hi all, I'm having a few problems with crystal dynamics of a simple monatomic chain. Taking the dispersion relation: \omega^2 = \frac{4k}{m}\left(\sin^2 \left( \frac{\kappa a}{2}\right)\right) Where k=spring constant, m=mass, \kappa=wavevector, a= lattice constant and \omega=...

Discrete Mathematics -- Symmetric Closure Math help in Numerical Analysis, Systems of I can't seem to find the way to approach this problem. Because it has symbols I don't know how to type here, I have attached an image here instead. Please help me if you can. Any input would be greatly...

Hi all, I have a function defined by an integral containing an arbitrary real parameter q. I can't do the integral, so I wanted to plot the function by evaluating the integral numerically. However, I can't do this owing to the arbitary-non numerical parameter in my integrand! Can anyone tell...

Hello there! I am solving a heat diffusion problem which is described by the differential equation: θΤ/θt=a*(θ^2Τ/ΘΤ^2). I will apply two diffrent temperatures on the ends of a metal rod. Solving the equation i conclude, according to the boundary conditions of course, at the function...

I posted this in the aerospace engineering forum but I think it may get more replies here: I've been trying to compute the bending-torsion coupling constants for a wing, B1, B2 and B3. The expression for this is \begin{bmatrix} B_1 \\ B_2 \\ B_3 \end{bmatrix} = \iint (y^2 +...

Homework Statement Plot the following parametric curve, defined by the following two polynomials, on the interval: t \in (-1;1). What shape do you get? x(t) = 16243t^{14} + 520143t^{13} -798515t^{12} -185877t^{11} + 150142t^{10} + 256559t^9 -135331t^8 -170995t^7 + 594415t^6 + 558842t^5...

I've written a Levenberg-Marquardt nonlinear optimization routine that employs the reverse-mode automatic differentiation algorithm for building the Jacobian. So far it has worked marvelously for me. However, now I have to use functions that contain integrals that cannot be analytically taken...

I have a system of first order pdes of the form dm/dt+f(m,n,a)dm/dx = g1(m,n,a), dn/dt+f(m,n,a)dn/dx = g2(m,n,a), da/dt+f(m,n,a)da/dx = g3(m,n,a). (those d's are partials) I want to solve them with the numerical MOC's so I put dx/dt = f(m,n,a), dm/dt = g1(m,n,a) etc and solve this system...

Homework Statement K(max) = (6.63x10^-34 J s)(7.09x10^14s) - 2.17x10^-19J solve for kmax Homework Equations none? The Attempt at a Solution K = (6.63x10^-34 J s)(7.09x10^14 s) - (2.17x10^-19 J) K = (6.63)(7.09)(10^-34)(10^14) J s^2 - (2.17x10^-19 J) K = (47.0067)(10^-24) J s^2...

Being a hobbiest programmer, I know enough about probability to get by. However, I've set myself an impossible (for me) calculation in my current personal project. I have a set of numbers. For this particular problem it is a set of four numbers {248, 184, 120, 56}, but I'll be repeating the...

Consider a new computer system which stores data in “quads”, i.e. it has four states 0, 1, 2 and 3 (as opposed to binary which has only two, 0 and 1). Now imagine that numbers are stored in a 12 quad format where there is one quad for the sign of the number, three quads for the exponent...

Hi! I have to solve a system of two coupled nonlinear ordinary differential equations. In the function that defines the system there are terms with square root of the dependant variables. I tried to solve the system numerically but in the nmerical solution I get violent oscillations. Then I...

Good evening, I have a background on one-variable Calculus and I am currently self-studying Calculus from Leithold's "The Calculus with Analytic Geometry". When I finish the part about infinite series, I plan to start studying Numerical Analysis. I would like to ask what book on Numerical...

I am kind of new to mathematica, and have checked the documentation but can't seem to find an answer. I have solved 3 coupled differential equations using NDSolve. I wish to integrate the solutions over a range but I'm not sure how to do it - the documentation seems to deal only with...

Homework Statement I have to build a 2D model of simple magnetic circuit, that is iron core (2) with coil(1) and air gap(3) applied to it. Model has to be solved on numerical basis, by finite difference or element method (whichever is easier to implement). Number 4 on drawing represents...

First of all, I apologize if this is in the wrong section. I would like to know what background is needed to be properly prepared for numerical analysis. I will have had calculus III (leaving C-4 left), ordinary differential equations. I'd be taking linear algebra concurrently. Also...

Homework Statement Well, I'm not sure if this is a correct subforum to post my problem, but to me it does seem to me as an academic problem. One I can not solve, apparently. Well, anyway. I'm solving the 1+1 radial wave equation using finite difference. I shifted my grid, so that the origin...