Numerical Definition and 701 Threads

In Matlab I am trying to use the composite Simpson's rule to find ##x_l## so that $$170=\int^{x_l}_0 \sqrt{1+(y')^2} dx = \int^{x_l}_0 \sqrt{1+\left( \frac{x^2}{68000} \right)^2} dx $$ For convenience this can be written as $$I(x) = 170 - \int^x_0 \sqrt{1 + (\frac{x^2}{68000})} dx$$ The...

I'm trying to solve numerically this multiple integral. But i don't know how to calculate it with Mathamtica or Sage software. $$\int{e^{-(\vec{v}^2_1+\vec{v}^2_2)}e^{-E(\tau)}}d\vec{r}_1d\vec{r}_2d\vec{v}_1d\vec{v}_2$$ $$E(\tau)=\frac{k}{\tau^2}e^{-\tau/\tau_0}$$...

I am trying to estimate the second derivative of ##sin(x)## at ##0.4## for ##h=10^{-k}, \ \ k=1, 2, ..., 20## using: $$\frac{f(x+h)-2f(x)+f(x-h)}{h^2}, \ \ (1)$$ I know the exact value has to be ##f''(0.4)=-sin(0.4)= -0.389418342308651.## I also want to plot the error as a function ##h## in...

Hey all, I seek to find where the derivative of a nth order polynomial is at a 0, so far I have used secant method to find it, which works, but issue is is that that returns only one root, sliding the interval could work, but then itd always point to the edge of the interval, any help...

Homework Statement Homework EquationsThe Attempt at a Solution So I am tasked with answer #3 and #4. I have supplied the indicated parenthesis of 8 also with the image. Here is my thinking: Take the Fourier series for |sin(θ)|. Let θ = 0 and we see a perfect relationship. sin(0) = 0 and...

i was trying to work with few problems for my computer oriented numerical method ...which i had in college ... i am not in college anymore ... but i failed that subject ... i am trying to improve this maths field as much as i possibly can , because its a difficult subject for me ... let met...

Hello. I have some questions regarding the equation: k\frac{\partial}{\partial x}\left( u\frac{\partial (u-r(x,t))}{\partial x} \right) = \kappa \frac{\partial u}{\partial t}. u is positive. r(x,t) is given as an input. I have implemented this non-linear diffusion equation using backward Euler...

Good Day Let's say I have developed a new method to extract, more efficiently (yes, "more efficiently" is ill-defined; but bear with me) the differential equations that describe a specific phenomena (please just assume it). So now I have a system of coupled second order differential...

I want to integrate a function numerically from 0 to infinity where for small x ##f(x)\sim x^{-5/2} \exp(-a/x)## and for large x ##f(x) \sim \exp(-bx)##. How do I best treat the steep rise for small x?

I'm an applied mathematician with lots of experience in classical physics but none in quantum physics. What's the simplest piece of code (eg C++ on Cygwin) that illustrates the https://en.wikipedia.org/wiki/Numerical_sign_problem in quantum physics?

I am studying numerical and programming course in this semester, I was asked to know the applications of this course (numerical methods like Bisection, Newton Raphson, Secant, Simpson, Euler and Lagrange) in geophysics and how can I exploit these methods in seismic or in geophysics in general...

Homework Statement Find the extremizing (maximum) value of the function f(x) = sin x / x using Newton's 1D method. Homework Equations [/B]The Attempt at a Solution I know the maximum point in this equation is (0, 1). When I differentiated the equation twice and used the formula above, I...

In the hidden variable model for CHSH, I computed the probabilities for the CHSH operators to have results -4,-2,0,2,4, then the average S. Using a computer program, I could find the minimum of that function, obtaining S>2 : #include<stdio.h> #include<math.h> double PI=4.0*atan(1.0)...

Hi! I would like to calculate the curvature for a surface S:R^2->R'3 numerically. The problem: I simply have the surface as a mesh like you see in the image attached. I calculated the linearly interpolated face normals in the nodes, too. You see the vectors. Question: How would you calculate...

Hi! Does anyone know where can I find the following thesis? M. Kyncl. Numerical solution of the three-dimensional compressible flow. Master’s thesis, Prague, 2011. Doctoral Thesis Thank you

Consider the case of a distributed computing system based on the processor-pool model that has ##P## processors in the pool. In this system, suppose a user start a computing job that involves compilation of a program consisting of ##F## source file ##(F < P)##. Assume that at this time the user...

I am modelling a 1D fluid wave propagation problem and I needed to know how I can check that my results are energy conservative. please reply, urgent. thank you.

Hi, Consider the conservation laws for an isothermal linear incompressible flow governed by the mass and momentum equation. The kinetic energy equation is then solved to see if energy conserved. Can anyone tell me if once it is shown energy is conserved, it implies that convergence is obtained...

Mod note: Removed the color formatting, and surrounded the code with [ code ] tags. @whatisreality, please use a tag at the beginning of your code, and a tag at the end. Inserting colors by hand is distracting and makes your code difficult to read. I have to write a piece of code to calculate...

Homework Statement I'm trying to write a program to solve a system of 3 non-linear equations using the Newton-Raphson method. I'm stuck on trying to figure out what the formula for a system of 3 unknowns is. I can't remember the derivation at all and after endless hours of googling and looking...

When will you consider that the numerical aperture is high? I was told that the numerical Angular Spectrum Method is only valid low numerical aperture values, I want to know the boundary of this value. Thank you in advance.

I am right now working on a script that solves the Schrodinger equation numerically for arbitrary potentials using the finite difference method. The idea is that I diagonalize the Hamiltonian with elements: H(i,i+1)=1/dx^2 * constants H(i,i-1)=1/dx^2 * constants H(i,i) = -2/dx^2 * constants and...

I am trying to numerically calculate the electric potential inside a truncated cone using the finite element method (FEM). The cone is embedded in cylindrical coordinates (r,phi,z). I am assuming phi-independence on the potential, therefore the problem is essentially 2D; I am working only with...

I have written a program that solves the Schrödinger equation numerically using the finite difference method based on the attached article. The end goal is to make a program that solves the Schrödinger and Poisson equations self-consistently for the conduction band in different heterostructures...

Homework Statement A large cylindrical vessel contains water to a height of 10 m. It is found that the thrust acting on the curved surface is equal to that at the bottom. If atmospheric pressure can support a water column of 10 m, the radius of the vessel is:- (a) 10 m (b) 15m (c) 5 m (d) 25 m...

Hello everyone! I am currently playing with an old analog computer, which could solve time-dependent ODE/PDEs pretty fast, without time-stepping. But the problem with analog computer's solutions is that they are not very accurate. I am very curious that is there any numerical method/solver which...

In computational physics is very often to calculate largest Lyapunov exponent. If largest Lyapunov exponent ##LE## is positive there is chaos in the system, if it is negative or zero there is no chaos in the system. But what can we say about some certain value of ##LE##. For example...

I believe I am misunderstanding the equations I must use for the Runge Kutta of an orbit in polar coordinates. What differential equations can i use which will allow me to numerically determine both an object's distance and angle in an orbit, dependent on time?

What are some good books (or other resources) on numerical methods of solving PDEs in 3 space and 1 time variable? I am interested both in finite element and finite volume methods. I could be interested in other methods but I don't know about them. I am interested in being able to take...

http://www.cpp.edu/~jlcannons/mat_201_2015_spring/Project_01.pdf I don't know if this counts as cheating, but I hope someone could look this over and see what my professor is ask.

Ok, I've built a numerical model to show the cooling of hot magma sills entered into the crust over time. The results show that the volume of the "hot" zone when the emplacement of a constant volume of hot sills is all done will vary as a matter of two things: the overall rate at which the magma...

Hello all, I would like to know how to impose a normalization condition to numerically solving an ODE. For simplicity let's consider the example \frac{dy}{dx}=y You could use different methods using an initial value, but if you consider the interval [x_0,x_1] and \int_{x_0}^{x_1} y(x)dx=1...

Hi PF! I have just solved a non-linear ODE numerically in mathematica using the "NDSolve" command over a small interval ##[0,1.5]##. I'd like to be able to fit a polynomial to this solution, perhaps using the "Fit" command, although I've had no luck on my own. Any help is greatly appreciated!

Hello everyone; i'd like some help in this problem : i want to solve num this differential equation { y"(t)+t*cos(y)=y } by the Taylor method second order expansion. i first have to make this a first order differential equation by taking this vector Z=[y' y] then we have Z'=[y" y'] which equal...

Hello! (Smile) Consider the initial value problem $$\left\{\begin{matrix} y'(t)=f(t,y(t)) &, a \leq t \leq b \\ y(a)=y_0& \end{matrix}\right. (1)$$ I want to write a program that implements the following numerical method to solve $(1)$ $\left\{\begin{matrix} y^{n+1}=y^n+h[\rho...

Homework Statement Calculate the magnetic field of a current loop. Compare your numerical results with exact solution above the center of the loop. Investigate the effect of the grid size based on this comparison. Homework Equations dB = u0*I/4pi * (dL * R) / (R^2 + Z^2)^3/2 Bz = u0*I*R^2/ (2...

Not sure whether to post this here or in QM: I trying to numerically solve the Schrödinger equation for the Woods-Saxon Potential and find the energy eigenvalues and eigenfucnctions but I am confused about how exactly the eigenvalues come about. I've solved some differential equations in the...

In two semesters or so, i will be taking a numerical analysis course as part of an Applied Mathematics major. In the course description it says that you should have knowledge of at least one programming language, but i cannot find any more information about this. What do you all think would be...

Hi, I'm asking this because I ordered this book today, but there is a 4-day shipping minimum. I have to do a few problems from this book, and if anyone owns this, is it possible to tell me the problem statements? Also, if I'm not allowed to ask for this, please let me know. The problems I...

hi guys i need some help with the iteration made in a numerical solution for the eigenstates in a finite square well potential using the effective length approximation First, i find the eigenstate for a infinite square well, then i define the related alpha and i use it to define an effective...

Hi Guys, I'm new on this forum, currently studying Aerospace Engineering and am trying to produce the model of a radioisotope thermoelectric generator using numerical methods to solve the heat conduction equation as part of my research. The way it works is that I have a radioisotope source in...

Hi, I am working on TDR (Time Domain Reflectometry). I send a 7GHz bandwidth fast rising edge (14ns) square wave into a coax. I get a return Signal. I have an ADC with 10Msamples/sec. I am using MPLAB IDE for coding the microcontroller. Now I would like to increase the Points on the...

Homework Statement During the first t seconds of motion, the average velocity of the point is zero. What is the numerical value of t? Homework EquationsThe Attempt at a Solution I don't understand this question. I understand that the average velocity is zero if the displacement in the...

I've been trying to figure out a way to get an approximation to a complex DiffEQ. dx/dt = c1 / (c2 + c3*x*t) Does anyone have any input on wether this problem can be approximated? Thank you.

Hi I am new member and I am new to the Signal processing so I hope I could get some help from the members to able to understand the concepts. I have a Signal. I have a 10Msaples/sec ADC. I view the Signal on an Oscilloscope which has 20Gsamples/sec sampling rate. The Point where I am...

I am taking a computational physics course, and currently I have very little knowledge of programming. I have downloaded the numerical recipes machine-readable code, and I am trying to get one of their examples to work in dev-c++. Unfortunately, I am having difficulty. I have copied xodeint.c...

This is a quite general question, but I am working with a system of partial differential equations in two variables. There is one time direction t and one spatial direction z and the numerical method is formulated by stepping forward in time. The problem is that I obtain instabilities, either at...

Hi - I have just started 'Computational Physics' by Koonin & Meredith, - through distance learning. Exercise 1.3 needs a program to evaluate an integral - I'm finding myself kinda rusty on integrals. The hint says - split range of integration into parts, use different change of variable in each...

So, I ve been trying to add orientation to my model of the flight dynamics of a rocket but I ve been running into a lot of problems. I didn't bother actually doing the math for the moments of inertia and everything because I guess it really doesn't have that much of an effect on the general...

In my computational physics textbook, three different velocity estimators are derived for a problem with equation of motion: \ddot x = F(x) where the positions are found by using the Verlet algorithm: x(t+h) = 2 x(t) - x(t-h) + h^2 F[x(t)] The three velocity estimators are: v(t) = \frac{x(t+h)...