Method Definition and 1000 Threads

Hello! I am having unexpected difficulties with this problem.A friend showed me an article regarding the Lecomde ring method,and at the bottom was this little problem that to solve.I've done it like this. $$ y = \frac{F}{4\pi r} $$ where F is the given force and r is = 0,0325 in meters. The...

Hi, first-time poster here I'm a student at HS-level in DK, who has decided to write my annual large scale assignment on Schrödinger's equation. My teacher has only given us a brief introduction to the equation and has tasked us to solve it numerically with Euler's method for the hydrogen atom...

Hey! :giggle: Question 1 : Let $g(x)-=x-x^3$. The point $x=0$ is a fixed point for $g$. Show that if $x^{\star}$ is a fixed point of $g$, $g(x^{\star})=x^{\star}$, then $x^{\star}=0$. If $(x_k)$ the sequence $x_{k+1}=g(x_k)$, $k=0,1,2,\ldots$ show that if $0>x_0>-1$ then $(x_k)$ is...

Hi PF! Do you know of any examples of the Ritz method which use Bessel functions as trial functions? I’ve seen examples with polynomials, Legendre polynomials, Fourier modes. However, all of these are orthogonal with weight 1. Bessel functions are different in this way. Any advice on an...

Goodd day, I have a question regarding an exercice I have already posted Bvu was very nice and provided this darwing I already have the solution But y question is : can we use the disk method? because as you can see even though the intersection was at x=-1 the sphere goes deep into the...

Good day I have the following exercice and it's solved using spherical coordinates I totally agree with the solution but I have issue to find out why mine does not work I used the the integration by disk I divided the region of integration to 2 A1 and A2 (A2 is the upper half sphere and A1 is...

Hi! I'm trying to understand and solve this circuit by Node Voltage Method. I have to calculate u(t). In my mind, I don't have any idea if any current should go through Z1 in my calculations. I would be grateful if you could write even equations for this circuit. Is 'a' just a prefix to multiply...

Each different boundary condition means a different charge configuration, how can this problem be solved using superposition?

This just to share a teaching experience. Questions about the method of characteristics are raised from time to time in this forum. Hope the following text will be of some use. This is what we tell to students in courses of analytical mechanics :)

I was asked to find the ratio of the fluxion of x to the fluxion of 1/x using Newton's synthetic method of fluxions. I do not understand how to do this.

Hello everyone, I have to submit an assignment by Monday and there is only one part of the assignment missing, which is future developments of the Explicit Finite Difference Method. However, I can not do it because I really do not know what exactly he is asking me for on there. Could someone...

We have to submit a Matlab (my worst module) assignment to show the heat transfer on a plate. However, I have the 2 codes almost done but I am struggling to write the report. To calculate the temperature on a 2D aluminum plate we need to use the Explicit Finite Difference Method. The problem...

I have come across this strange method of solving degree 2 polynomials but I do not find the explanation provided to be very helpful. Here is the method description: "In the 16th century, mathematician Francois Viete solved quadratic equations by a unique substitution method. To solve an...

hi guys i was trying to solve this non linear ode using the shooting algorithm in Matlab : i am not sure how to solve it using the normal shooting algorithm i have , since no other boundary at x = L/2 was given to check the shooting ?! function dTdx = bar_temp(x,y) k = 72; h = 2000; epsilon =...

Summary:: Initial value problem Solve the given initial-value problem differential equation by undetermined coefficient method. d^2 x/dt^2 + w^2 x = F sin wt , x(0) = 0, x'(0) = 0 I get the sol = C1 cos wt + C2 sin wt, but i always get 0 when I plug into the equation, anyone can help me...

I'm trying to write a C++ program to generate random numbers using the acceptance-rejection method. To plot the graphs, I'm using ROOT by CERN. I am checking if y values taken from the rectangular boundary are less than or equal to the function ##f(x_{i}) = e^{-k(x_{i} - x_{0})^{2}}##. void...

Hey! 😊 I have calculated an approximation to $\frac{\pi}{2}$ using Newton's method on $f(x)=\cos (x)$ with starting value $1$. After 2 iterations we get $1,5707$. Which conditions does the starting point has to satisfy so that the convergence of the sequence of the Newton iterations to...

Hi guys, I'm being introduced to magnetism, and the direction of the Lorentz force is quite confusing since it's involving a vector product. Which method would you recommend me in order to easily deduce the direction?

Can you help me with this question ? I am really struck with this question. Thank you in advance.

Can you check it for me please that I have done it right or not ? Thank you in advance.

Can you check it for me that I done it right or not ? Thank you in advance.

The problem is to solve for the area R. Can you please help me ? I have tried to do it many times. Thank you in advice.

Can you please help me ? I have tried to do it but I end up getting the wrong answer.

I need to solve the following equation for [OH-]: Kw/[OH-] + (10^-5)Kb/(Kb+[OH-]) = [OH-] by using the iteration method. I guess that [OH-] = 10^-7 M. I plug this into the left hand side of the equation and find [OH-] = 1.39*(10^-7) M. I plug this value back into the left hand side, and get...

Hi all, I'm working on programming a simple 2D method of characteristics program to design the nozzle wall contour for a supersonic rocket nozzle. I'm wondering roughly what sort of difference I should expect from a 2D vs 3D method of characteristics program and where I could find a good...

I'm trying to find the local truncation error of the autonomous ODE: fx/ft = f(x). I know that the error is |x(t1) − x1|, but I can't successfully figure out the Taylor expansion to get to the answer, which I believe is O(h^3). Any help would be greatly appreciated!

A conducting sphere of radius a is made up of 3 different shells, upper part a/2 z -a/2, the middle part -a/2 z a, the lower part -a z -a/2 where the center of the sphere is at the origin. The upper part V and the lower part has -V potentials, while the mid part is grounded. Find the...

I'm really stuck on this one, I was able to get the answer but not by the substitution method. So its the weight as A and B so I get A + B = 24 A(3) = B(5) so in my head I calculate a few pairs, 3 x 5 = 15 but 3 + 5 only = 8 so the next pair would be 10 and 6 which is still to small so I move...

My question concerns what I call R.P.S. (Rotating Planing Surfaces). This version uses freely rotating disks to plane across the surface of the water somewhat similar to wheels on a car going down the road. Specifically what the lift / drag ratio might be and will it be higher than a typical...

although we cannot change the syntax of the main() method but programmer does create main() everytime in the program.so i want to ask if it should be pre defined method.

Given are two equations: $$S_1 = ax^2+2hxy+by^2 + c=0$$ $$S_2 = a'x^2+2h'xy+b'y^2 + c'=0$$ This source states that there are several methods to solve for ##x## and ##y##. One of them is the following quote:"Treat equation ##S_1## as a quadratic equation in ##x## and solve it for ##x## in terms...

Differentiating eq1 mentioned above, and using eq 2, i got : $$v\frac{dv}{d\theta}=R\frac{dv}{dt}$$ From this, i got:$$ \frac{d\theta}{dt}=\sqrt{(2/R)(g(1-cos\theta )+asin\theta)}$$ After this point, I am not able to understand what substitution or may be other method could be used to solve...

ƒ(x,y) = 3x + y x² + 2y² ≤ 1 It is easy to find the maximum, the really problem is find the minimum, here is the system: (3,1) = λ(2x,4y) x² + 2y² ≤ 1 how to deal with the inequality?

I recently encountered mirror symmetry method of solving circuits and by it solving circuits became very easy but problem I am facing with it is that I can't figure out logic behind it. For example if we try to simplify this circuit Then we say that if ##I## current flows from Point A to C then...

Question: So I got around on doing this example, and I'm pretty sure I messed up somewhere, would appreciate if someone could point out what I did wrongly. 1) For any second ODE, I should let: ##y_{1}= y ## and ##y_{2}= y' ## Hence, ##y_{1}'= y' = y_{2} ## and ##y_{2}'= y'' = xy(x)+x^2-y(x) =...

This approach is seeming intuitive to me as I can visualize what's going on at each step and there's not much complex math. But I'm not sure if I'm on the right track or if I'm making some mistakes. Here it is: ##A## has set up a space-time co-ordinate system with some arbitrary event along his...

I use the operator method here: (D^2 + D+3)y = 5cos(2x+3) ## y = \frac{1}{D^2+D+3} 5cos(2x+3) ## ## \Rightarrow y= \frac{5}{-(2)^2+D+3}cos(2x+3) ## ## \Rightarrow y= \frac{5}{-4+D+3}cos(2x+3) ## ## \Rightarrow y= \frac{5}{D-1}cos(2x+3) ## At this, if I revert back to write: (D-1)y = 5cos(2x+3)...

This problem came from Problems, Section 3 Chapter 7 in ML Boas, Mathematical Methods in Physical Sciences. Boas suggested to make a computer plot. From my computer plot (I use online graphing calculator) and find that the period of the sum is 2. Instead of using computer, I want to find the...

Hi everyone! I am studying spectral methods to solve PDEs having in mind to solve a heat equation in 2D, but now i am struggling with the time evolution with boundary conditions even in 1D. For example, $$ u_t=k u_{xx}, $$ $$ u(t,-1)=\alpha, $$ $$ u(t,1)=\beta, $$ $$ u(0,x)=f(x), $$ $$...

This is for my Engineering master project. I am doing a feasibility study on a couple of different designs of small gas fuelled power stations for remote areas. A big part of it is the CAPEX costs. Most companies hold that kind of info very closely. Does anyone have any insights on this kind...

Excellent read on the brokenness of the scientific method: there are many, many issues, ranging from conflicts of interest, data falsification, lack of proper incentives, abysmal lack of statistical knowledge, etc. As many as HALF of scientific papers published today might simply be wrong! In...

Hello all, this question really has me and some friends stomped so advice would be appreciated. Ok so, the relevant (dimensionless) continuity equation I have found to be $$\frac{\partial\rho}{\partial t} + (1-2\rho)\frac{\partial \rho}{\partial x} = \begin{cases} \beta, \hspace{3mm} x < 0 \\...

I feel like i am spinning my wheels at the start here. so I figured that i would start with some type of wire loop that I could change its diameter. This would allow there to be a change in flux through the loop creating a current through the wire. i could then read the current through the...

Hey! :o A point is moving linearly with constant velocity $v$ and the movement is $x=a+vt$. The below information is given: Find the initial position $a$ and the velocity using the method of least square. Could you give me a hint how we use this method here? Couldn't we use the data of...

I oriented a magnetic dipole perpendicular to the hole (parallel to the [FONT=STIXGeneral-Italic]y[FONT=STIXGeneral-Regular]̂ [FONT=STIXGeneral-Italic]y[FONT=STIXGeneral-Regular]̂ y^[FONT=STIXGeneral-Italic]y[FONT=STIXGeneral-Regular]̂ direction) with one end at it's origin and I get the...

Hey! :o The function \begin{equation*}f(x)=\frac{x}{e^{x/9}}\cdot \frac{\sin \left (\pi (x-1)\right )}{x-1}\end{equation*} has at exactly one position $\overline{x}>1$ the same value as at the position $x=1$. Determine the position $\overline{x}$ using an iteration method with accuracy of two...

The Secant Method is a numerical scheme to solve equations of the form $\displaystyle f\left( x \right) = 0 $, so we must rewrite the equation as $\displaystyle 0 = \frac{1}{2}\,x^2 - 10 - \sin{ \left( 1.8\,x \right) } $. Thus $\displaystyle f\left( x \right) = \frac{1}{2}\,x^2 - 10 - \sin{...

Alexander asks: Apply three iterations of Newton's Method to find an approximate solution of the equation $\displaystyle \mathrm{e}^{1.2\,x} = 1.5 + 2.5\cos^2{\left( x \right) } $ if your initial estimate is $\displaystyle x_0 = 1 $. What solution do you get?

The Bisection Method is used to solve equations of the form $\displaystyle f\left( x \right) = 0 $, so we need to rewrite the equation as $\displaystyle 8\cos{ \left( x \right) } - \mathrm{e}^{-x/7} = 0 $. Thus $\displaystyle f\left( x \right) = 8\cos{ \left( x \right) } - \mathrm{e}^{-x/7} $...