Method Definition and 1000 Threads

In mathematics and computational science, the Euler method (also called forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who treated it in his book Institutionum calculi integralis (published 1768–1870).The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size.
The Euler method often serves as the basis to construct more complex methods, e.g., predictor–corrector method.

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  1. F

    Ambiguity in the method applied for differential equations

    Homework Statement Why do we need two solutions to solve a 2nd order linear differential equation? lets consider a differential equation with equal roots for auxiliary equation. So the reasoning behind why can't we use y=Aen1x+Ben2x as its general solution is because since the roots are equal...
  2. D

    I Generating polynomials for a multistep method

    Hi, I'm struggling to understand how the generating polynomials work and are implemented in the difference equation for a general ODE y' = f(t,y) Difference Equation Generating polynomials "Coefficients are normalized either by a_k = 1 or sigma(1) = 1
  3. D

    Stability function for a basic RK method

    Homework Statement Hi, can someone explain how they get this stability function. Homework Equations http://blob:http://imgur.com/840ee1fe-f09c-49ab-bdbb-7f953777f900 The Attempt at a Solution I have attempted to do it two ways, and I'm not sure if I'm just having an awfully bad day at maths...
  4. Leonardo Machado

    Problems with Runge-Kutta method

    I'm writing a program to compute an ODE solution of the Kepler's problem based on Runge-Kutta 4th order method and today I've past the whole day trying to made it work, but I've failed, maybe you could help me to kill the problem ? The solutions is cartesian. int main(){ int n...
  5. S

    JavaScript What is wrong with my method for predicting the election?

    Given the fact that there are 51 states and districts, there are 251 subcollections of the 51 states, which I can't possibly iterate over entirely. So what I do is find 210 subcollections of states whose electoral votes summed are 270 or greater. I then sum together the probabilities of Trump...
  6. M

    Particle-in-cell method vs. PM/PPPM methods

    I'm doing a paper on the particle-in-cell method, which was designed by Harlow and Evans in the mid 50s. But I'm reading Hockney and Eastwood's book Computer Simulation Using Particles in which they describe their models, and term them PP (particle-particle), PM (particle-mesh), and PPPM...
  7. AwesomeTrains

    Rayleigh–Ritz method - Yukawa coulomb potential

    Hello everyone Homework Statement I have been given the testfunction \phi(\alpha, r)=\sqrt{(\frac{\alpha^3}{\pi})}exp(-\alpha r) , and the potential V(r,\theta, \phi)=V(r)=-\frac{e^2}{r}exp(\frac{-r}{a}) Given that I have to write down the hamiltonian (in spherical coordinates I assume), and...
  8. C

    Need the derivation/proof of the method

    Homework Statement The method given in my book is to find the square root of a quadric surds is to : Consider a and b where both are rational and √b is a surd Equate the square root of a+√b to √x+√y ie (a+√b)^(1/2)=√x+√y Squaring both sides we get a=x+y and b=2√xyHomework EquationsThe Attempt...
  9. Jefffff

    Best Method of Analyzing Experimental Percent Error

    Homework Statement I have performed a chemistry experiment where I analyzed how the diluting of two reactants with the same volume and initial concentration impacts the percent yield of a precipitate product. Thus my IV was concentration and my DV was percent yield. My question is what is the...
  10. T

    Method of Joints Query: Shedding Light On Truss Calculations

    Hello all, I have recently been attempting to refresh my memory in regards to method of joints and have been making some reasonable progress, however I have ran into a stumbling block that has left me quite puzzled. I have been using the Skyciv truss calculator to verify my work and for the...
  11. M

    Rotational Volume Using Shell Method

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  12. VMP

    Solving Method of Images Problem for Induced Charge

    Homework Statement We have a coordinate system (x, y, z). Two conducting plates 1 and 2 are parallel and lie in the x-y plane. Plate 1 is at height (x, y, 0) and plate 2 is at height (x, y, 4a), where a is an arbitrary constant. Between these two plates there are 2 charges +q and -q. Charge...
  13. W

    Hardy Cross method correction problem

    Homework Statement I have problem with the flow rate (Q) in junction that join 2 loops together , where k = 4 , Why in the second correction , the corrected Q in first and second loop = 21 clcockwise for left loop , and for 21 anticlockiwise for right loop ? Homework EquationsThe Attempt at a...
  14. J

    Bode Plot Method For a Transfer Function

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  15. C

    Nuclear Reactor Simple 1D Method of Characteristics Solver

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  16. Swapnil Das

    Method of Symmetry for Equivalent Resistances

    I have been studying the method of symmetry from some days, which essentially reduce the effort needed for the evaluation of equivalent resistances. My textbook states: Points having symmetrically located about initial and final points have the same potentials.So, the resistances between these...
  17. F

    What value should be used for junction CA in the Hardy Cross method?

    Homework Statement i have a netwrok of pipe as shown in the figure . I'm asked to find the flow rate using HARDY CROSS method . in the second trial of first loop at junction CA , which value should i use ? -15.3 from the corrected in second loop ? or 22.7 from the corrected value in the first...
  18. F

    Using corrcted value for Hardy Cross method?

    Homework Statement i have several example of hardy cross problem involve 2 loops , for the junction that divide 2 loops , is it necessary to use the corrected value for the junction on second loop for the first trial ? or just use the initial assumption will do ...
  19. Telemachus

    Numerov method on a exponential grid mesh

    Hi there. I was trying to implement Numerov method for solving second order differential equations (you can see some information of Numerov algorithm at here: https://en.wikipedia.org/wiki/Numerov%27s_method ). At the beginning I've used a uniform grid mesh, all points equally spaced. I'm...
  20. W

    Understanding solution method for finding accelerations in a mechanical linkage

    Homework Statement I was checking my work and Chegg uses the equations differently. Can somebody tell me why? Maybe I'm misunderstanding how/why to use the equation I chose. Homework Equations They say aB = -ω2ABRB/Ai I used aB = aA + αk x r - ω2rB/A The Attempt at a Solution So obviously...
  21. C

    Method of joints for bridge truss

    Homework Statement Calculate the forces for each member. Homework Equations Sum of forces in x=0 Sum of forces in y=0 Sumof moments about D=0The Attempt at a Solution Work is on attached image of problem. I'm having trouble solving for support reactions. At D there is [/B] a hinge. At A...
  22. N

    A Numerical solution to SE - variational method, many electrons

    Hi everyone, I am trying to find electron wavefunction of a system I am working in. Numerical method I choose is the Variational method (VM). This method is convenient to find the ground state of the system. More details are available here. Problem I have can be explained on a very simple...
  23. Telemachus

    Variable grid mesh in Numerov's method (Fortran)

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  24. Xico Sim

    I Method to know if a reaction is allowed

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  25. rtd

    B Parallex Method: Struggling in 11th Class?

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  26. N

    A Solving forced PDE with method of Characteristics

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  27. Z

    What is a method to find the fundamental frequency of a pipe

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  28. abdulsulo

    I Whammer method of characteristics

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  29. P

    Analysis method to describe impact of variables on parameter

    Hi, I have an optical model, fully programmably controllable with python. I want to know how much my variables (say N) of my model impact a certain parameter (i.e power, abberations). Now I have no clue how to go about this. There must be some analytical (numerical) method that I could use but...
  30. R

    Secant Method Minimum Estimation

    Homework Statement I am having some trouble understanding the following solved problem: Use two iterations of the Secant method to estimate where ##x^2 -x## has a local minimum. Start with ##x^{(0)} =1##, ##x^{(1)} =1/2.## Answer: Homework Equations Secant iteration: $$x_k = x_{k-1} -...
  31. S

    Kirchoff's method for a weird circuit

    Homework Statement In the following circuit, the battery has emf ε = 12.7 V. The resistors are R1 = 2000 Ω . R2 = 3000 Ω, and R3 = 4000 Ω. What is the current through resistor R2 ? Homework Equations Kirchoff's Rules V=IR The Attempt at a Solution i0 (into A) - i2 (current into resistor 2) -...
  32. R

    MATLAB Bisection method and numerical integration

    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...
  33. Vajhe

    Computational Resources for learning about Optical Beam Propagation Method (BPM)

    Hi, I'm a physicist intern that has some problems with Optics simulations; I'm very interested in doing some Beam Propagation Method (BPM) simulation, but the information online is not that good for begginers in the area. Can anyone advise me on books, journals or such that might help me learn...
  34. D

    B Simple cheap method of measuring mass distribution of object

    I'm looking to measure the weight of an tennis racket at different lengths. Obviously If I stick it on the scale it will give roughly the sam,e weight no matter if I put the whole racket on, or a third of the racket. Would there be a way I could measure the weight, of say the first third of an...
  35. Iqbal94

    I Approximating and regression method

    Hi guys, I did a few sets of test in determining the natural frequency of a crane lifting loads. From that, I tried to find two constant from its initial function. a is the stiffness of the pole that was holding the crane b is the weight of the crane x is the weight of the load The tests...
  36. R

    MATLAB How can I fix the dimensions mismatch in my split-step Fourier method code?

    I am trying to write a very basic Matlab code to preform the split-step Fourier method on the nonlinear Schrodinger equation: $$\frac{\partial A(z,T)}{\partial z} = -i \frac{\beta_2}{2} \frac{\partial^2A}{\partial T^2} + i \gamma |A|^2 A \ \ (1)$$ I want the program to make 3D plots of...
  37. M

    Method of succesive smoothing in triangular geomtery

    Dear all I want to know a formula in order to calculate corner point flux using surface and volume averaged fluxes in triangular geometry. I studied some papers from Finneman and et. al., but I could not find the necessary formula. I have attached a file about my quastion. Thank you
  38. D

    Need a device or method to generate cool air outside

    I need a way to generate cool air outside when temperatures are 90s and above. Basically what I am thinking of doing is essentially like positioning a fan right beside a bowl of ice cubes. Only in my case, instead of using ice cubes, an electrically powered cooling device that can slightly...
  39. U

    I Revolutionize Space Travel with Innovative Vacuum Launch Method

    I know magnetic launch tracks on the side of mountains has been proposed before but what if... you vacuum the inside of the launch track on the side of the mountain and extend the tube up from about 5K meters to 30K meters? The tube on the side of the mountain would be made of a strong metal...
  40. B

    List of quantitative methods for optimization

    Max: 3x + 5y s.t. x + 2y ≤ 5 x ≤ 3 y ≤ 2 x,y ≥0 By the simplex method, the profit is $14. Using sensitivity analysis I changed the RHS of the 1st constraint and keeping everything else constant, I get the best profit value of $19 at RHS of 7. What other methods can I use such as the...
  41. P

    B Most Efficient Method for Counting

    I'm talking about different bases here. I've heard a bunch of people say that base 12 is the best way to go, since it would make basic math easier. After all, 10 from the decimal system has only 4 factors (1,2,5,10), whereas 12 from the duodecimal system has 6 (1,2,3,4,6,12). But, looking from a...
  42. Shailesh Pincha

    I Rotation curve of galaxy Keplerian method

    There are 2 unknowns in the formula. The time period of rotation and the mass enclosed by orbit is Star. So how could we calculate the expected time period of rotation of stars in a galaxy and thus velocity of stars.
  43. R

    Why are potentiometers not a good method of speed control

    Why are potentiometers not a good method of speed control(in terms of energy)?
  44. G

    I I found a *useful* method to calculate log(a+b), check it out

    So, I found this method, I don't think I was the first to, though, but I don't see any post related to this anywhere on the internet, so maybe there's a slim chance I was the first? Anyway, it doesn't really matter. The method does not give the precise result, only approximations, but I find it...
  45. V

    Determination of Rydberg Constant via Graphical Method

    Homework Statement Not sure if this belongs in the 'Advanced' section so apologies if it does not. I am using a monochromator to measure spectrum lines from a rubidium lamp. From the data (wavelength of spectral lines plus transition number 'n') I am asked to use a graphical method to...
  46. A

    Understanding the method of Green's function

    I'm trying to understand the derivation for methods of Greens functions for PDEs but I can't get my head around some parts. I'm starting to feel comfortable with the method itself but I want to understand why it works. The thing I have problem with is quite crucial and it is the following: I...
  47. O

    Volume of Revolution By Shell Method.

    Homework Statement Find the volume of the solid obtained by rotating y=x^2 and x = y^2 about y=2 Homework Equations V= 2πrh The Attempt at a Solution When I had constructed the graph I determined the following: r= 2-(y(1/2)) h= 1-y2 after converting V into an integral I applied fundamental...
  48. N

    Simulating Free Fall Using Euler's Method in C

    Homework Statement Write a C program to simulate a falling object. The program should ask for the initial height of the object, in feet. The output of the program should be the time for the object to fall to the ground, and the impact velocity, in ft/s and miles/hour. Your program should use...
  49. B

    Induction motor control by DTC method

    I´m simulating an induction motor control using DTC (direct torque control). I want to tune my PI controller to achieve a fast start up, but I don't have a transfer function to make an analysis. How can I set this controller?
  50. F

    Method of images about a sphere with a dipole

    Homework Statement Hello everyone, I am new here and have a question regarding method of images in my electricity and magnetism class. I need help to even get the ball rolling. The question is as follows: a) What is the image of a dipole, oriented toward the center of the conducting sphere, if...
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