Numerical Definition and 775 Threads

Hello, Is there a difference from these courses, or are they the same course with different names? I need to know which one to choose for the upcoming semester... Intro to Analysis, Intro to Real Analysis I, and Numerical Analysis Thank you, Tracie

I would like to solve the following differential equation, it seems easy but only given one initial value. y''(x) = ln(ln(x)) y(5) = 0 Solve for y(10) I know it can be directly integrated but cannot be expressed in terms of elementary functions. Most numerical method involves expressing the...

Hello everyone I have the following question regarding numerical integration twice from acceleration to displacement. Suppose that a particle has acceleration function of a = tt (which has non-elementary integral), to find the velocity it is easy as I can use Simpson's rule for numerical...

Homework Statement The differential equation of motion for the simple pendulum can be shown to be ##\ddot {θ} = -(g/L)sinθ##. Given that L=9.81 m and that the pendulum is released from rest at θ=60deg, determine the time required for the pendulum to reach the position θ=0deg. Use Δt=0.10s, and...

Hello, I am dealing with a function f(x) involving various complicated trig functions. I took the first derivative of the function f(x), which is doable, and set it to zero to find the at which value x the function f(x) would be maximum. However, once I have the derivative of f(x), it does not...

The question is very general and could belong to another topic, but here it is. Suppose one wants to solve the set of differential equations $$ \frac{\partial x}{\partial t}=\frac{\partial H(x,p)}{\partial p},$$ $$\frac{\partial p}{\partial t}=-\frac{\partial H(x,p)}{\partial x},$$ with some...

Homework Statement So this is a problem for my numerical methods class. We are doing integration and derivation. The part that I am stuck on is why does the midpoint method and trapezoidal method both have error of order ##h^2##, when the first one is one point integration method while the...

Homework Statement Homework EquationsThe Attempt at a Solution a) t' = l0/c b) ct1 = l0 /ϒ - vt1 t1 = l0 /ϒ(c + v) c) t2 = l0 / (ϒ v) Is this correct?

Homework Statement Homework Equations 1) k.e. = (1/2)mv2, non- relatvistic 2)K.E. = m0 c2 (ϒ -1), relativistic 3) L=L0/ϒ , Length contraction The Attempt at a Solution (A) Taking 1019 eV to be the kinetic energy of the proton, Non- relativistic calculation (1/2)mv2 = 1019 eV = 1.6 v =...

1. Homework Statement Hello all. It is not a homework actually. I just didn't know at which forum I should post. I am working on a MATLAB code solving the finite wing properties iteratively by using the Anderson's Numerical Lifting Line Method. However, I got some wrong results. The...

https://www.amazon.com/dp/1305253663/?tag=pfamazon01-20 Are all these called root finding algorithms? All of it ? <Moderator note: Link changed because of undetermined copyright situation. fresh_42>

Can anyone help in the solution of this problem? how can i determine the zero x*??

I think I understand the relationship between the three, but I would like some feedback. I still am fairly unsure about lens speed and is what I'm mostly interested in. From my understanding: Aperture is the total diameter of the lens and numerical aperture is the ratio between the aperture and...

Homework Statement I have a problem with my physics task, but you do not need to understand physics to be able to help me, because my main problem is bad programming skill. I am dealing with a problem of throwing a ball in the air at an angle between 0 an 45 degrees. I need to consider not only...

Can anyone recommend a good textbook or article for numerically solving general relativity problems? Say for a planet orbiting a pair of binary stars, or even for the sun and Jupiter in our solar system?

A little question about the appropriateness of a certain research subject... Would it be useful to make a study of the computational effectiveness of equivalent codes written with Matlab, Mathematica, R Code, Julia, Python, etc. in a set of typical computational engineering problems like...

So I am working out a course schedule for my last two years of undergrad and have room for only one more math class but do not know which would be more beneficial. The two courses are Intro to Modern Algebra or Numerical Linear Algebra. I am working towards a bachelors degree in physics and plan...

Until now, I have always think of Matlab as CAS but now I know that it is not. So how do you understand this? Thank you.

Context: In James Hartle's Gravity, pp. 318-319, Example 15.1, he considers the case of a particle that starts falling from infinity into a Kerr black hole, initially with no kinetic energy (e = 1) and initially moving radially (ℓ = 0). The particle's motion is constrained along the equatorial...

Could you recommend books which covers extensively numerical simulation of quantum system, such as hubbard model, ising model and discuss quantum monte carlo method? Ideally this is a book of condensed matter physics.

Hi! I'm trying to understand how to diagonalize a Hamiltonian numerically. Basically I have a problem with a Hamiltonian such as H = \frac{1}{2}c^{\dagger}\textbf{H}c where c = (c_1,c_2,...c_N)^T The dimensions of the total Hamiltonian are 2N, because each c_i is a 2 spinor. I need to...

Hi I am trying to verify my manual solution for this problem by any way, so I tried NDSolve, and DSolve, in mathematica with no success. I don't need it in mathematica I just need any way poosible, even matlab, or any other numeric way/soltuion. Can some one help, or even give me the final...

From cosmology, the tensor to scalar ratio is ##r=16\epsilon## where ##\epsilon=-\frac{\dot H}{H^2}## is the Hubble slow roll parameter. From warm inflation, $$\ddot \phi + (3H+\Gamma)\dot \phi + V_\phi = 0 ,\quad H^2 = \frac{1}{3M_p^2} (\frac{1}{2} \dot \phi^2 + V)$$ where ##H## is the Hubble...

Hello, What is the numerical formula for a derivative, considering the x's are not in the same distance?

Hello! Could you tell me about how to take the next numerical calculation in mathematica? (perhaps there are special packages). I have an expression (in reality slightly more complex): ## V=x^2 + \int_a^b x \sqrt{x^2-m^2} \left(\text Log \left(e^{-\left(\beta...

A question for those who are computational physicist: Dear Computational physicist, I am struggling between computational physics course or numerical analysis. They are both in graduate level (so very intensive), one in physics department and another in math. Both are taught by leading experts...

I'm very new to Mathematica/programming and I want to do a theoretical calculation using Mathematica, suppose I have, ##Y=CX,~~~C=constant## Now, I want to plot Y vs. X but X should run at every point since every point is a solution for Y, how should I do this? Before, I was thinking maybe I...

Suppose I want to solve the Schrödinger equation numerically for some potential V(x). The easiest way to do so, is to discretize it on a grid of finite length, and apply a finite difference scheme to approximate the second order derivative. Doing so yields an eigenvalue equation on matrix form...

hi all ! i'm trying to solve numerically the chua circuit set of differential equations , I am using the equations showed in this pdf: http://nonlinear.eecs.berkeley.edu/chaos/RobustOpAmpRealizationOfChuaCircuit.pdf i have the real circuit mounted and I'm using its parameters for the numerical...

Homework Statement Hi all! I'm having trouble understanding the implementation of some derivatives in the expression (1) of this article: https://www.ncbi.nlm.nih.gov/pubmed/26248210 How do I implement ∑(ij) ∂ijw ? Thank you all in advance. Homework Equations w is a square matrix(120x120)...

Hi there. I have to solve a system of coupled ordinary differential equations. I have some initial values, but in different points of the domain. The equations are all first order. Let's suppose the system looks like this: ##\displaystyle\frac{dy_1}{dz}=y_1+y_2+0.01##...

I attempt to solve the brachistochrone problem numerically. I am using a direct method which considers the curve ##y(x)## as a Lagrange polynomial evaluated at fixed nodes ##x_i##, and the time functional as a multivariate function of the ##y_i##. The classical statement of the problem requires...

Homework Statement We need to write an integrator for the Chandrasekhars Equation (CE) for White Dwarfs (WD) using python3/NumPy/Matplotlib. We then need to compute the structure of a WD made of our varying elements. We also need to compute and plot the mass-radius relation for WD. Homework...

Homework Statement I have a discrete two-dimensional velocity field (u,v). I want to plot the streamlines by finding the streamfunction ψ and from that plot the streamlines by finding the curves where ψ=constant.Homework Equations In order to find ψ I then have to solve the equations (see link)...

Hi Guys, I'm trying to do a simple first-order, 1d (x-direction) simulation of mass transfer with the finite element toolbox in MATLAB for the following closed set of equations: (Please note: "X" is not to be confused with the lowercase spatial dimension "x") However, every time I...

Homework Statement In this problem you will do numerical computer calculations. A skydiver of mass 75.0 kg jumps out of a plane at an altitude of 30.0 km above the surface of the Earth. His parachute fails to open. Assume there is no horizontal motion and the initial velocity is zero. We...

Is their a tutorial or a reference on how to decompose a function, specifically Fourier and Legendre decomposition, for numerical integration? The method I am going to use for the numerical integration is the Gauss Quadrature, and I suppose I need to decompose my function for the rule to work...

What are useful practical applications of numerical conformal mapping that are most limited by map computation speed or boundary complexity? I'm betting some of the applications will be be physics PDEs, so I chose this DE subforum to ask. As part of an engineering project I've implemented...

I have a Masters in pure mathematics and wanted to do my PhD in the areas of category theory, homotopy theory, and related fields, but I was not accepted into any programs despite not trying to attempt at all for the "brand name" schools and aiming for what I believed were the less competitive...

Hi,I'd like to build a simulation (realtime) of space ships near a black hole (neutral, still or rotating possibly). Key features would be: 1) the ships are test particles that do not affect the metric a) possibly test rigid-bodies with GR consistent rotational DOF. 2) the ships can fire...

I am currently working through Spivak, and have finished Geometry by Moise. I wanted to learn numerical analysis on my own. I could take it at the university, but I rather use the elective for differential geometry. What are good books on Numerical Analysis? I have completed 2 books in Linear...

Hi, I am trying to analyze the an harmonic oscillator using kinematics. first i calculate the force applied by the spring (f = (-x)*k) then i calculate the acceleration (a = f/m) then speed (v= v0 + v0t + 0.5*a*t^2) and finally update x (x = x0+vt) this is a simplfied loop of my program...

what are all the algorithms involved in finding a solution with numerical methods ?

i have few more doubts about these two numerical methods type questions ... An equation containing the derivatives of one or more dependent variables, with respect to one or more independent variables, is said to be a differential equation a question usually starts like this ... find the...

i have few doubts about differential equations and numerical methods ... in a differential equation question ... you are given an instantaneous rate of change... and you are supposed to find the function that gives , this instantaneous rate of change is this same as ... f(0)=1...

A Proton Of Mass 1.67*10^-27kg And Charge 1.6*10^-19c Moving At An Initial Speed 3*10^6m/s Against A Uniform Electric Field Has Its Speed Reduced By 50% After Covering A Distance Of 1.0cm In The Field. Determine The Strength Of The Field? ‪help me solve this problem what formula should i use to...

I am looking to numerically solve the (complex) Time Domain Ginzburg Landau Equation. I wish to write a python simulator to observe the nucleation of fluxons over a square 2D superconductor domain (eventually 3D, cubic domain). I am using a fourth order Runge Kutta solver for this which I made...

I think I am missing something painfully obvious, but what exactly is the difference in algorithms used to solve PDEs vs ODEs? For example, I've been looking at finite difference methods and the general steps (from what I've seen, although particular approaches may vary) used to numerically...

Hi there. I want to evolve a system of non linear coupled ODEs \frac{dx}{dt} = \frac{-k}{x^5(56-y^8)^{9/2}}(85+y^{5} + y^{6}) \frac{dy}{dt} = \frac{-k}{x^4(56-y^5)^{7/2}}(44+y^2) Let's say I have the initial conditions. What numerical method someone could use to solve this? adaptive step...

Suppose we are solving a diffusion equation. ##\frac{\partial}{\partial t} T = k\frac{\partial^2}{\partial x^2} T## On the domain ##0 < x < L## Subject to the conditions ##T(x,0) = f(x) ## and ##T = 0 ## at the end points. My question is: Suppose we solve this with some integration scheme...