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.

View More On Wikipedia.org
Recent contents Top users
  1. M

    Learn Euler's Method for Pendulum Simulation | Excel Tutorial

    This is not part of my homework, but it can make my life much easier. I try to prepare the Excel file as instructed in the link, but I can not find information on how to get the correct value of Theta Dot. http://www.esm.psu.edu/courses/emch12/IntDyn/course-docs/Euler-tutorial/ I'm sorry that...
  2. S

    Plate Buckling Deflection Function for Rayleigh Ritz Method

    G'Day Everybody, I am computing buckling of a rectangular(edges: a*b) specially orthotropic composite plate. The boundary conditions are clamped-clamped at the opposing loaded edges and the other two edges are free (also known as CFCF). After having the boundary conditions and the governing...
  3. P

    MHB Largest remainder method

    Hello All, I'm working on a problem which uses the largest remainder method https://en.wikipedia.org/wiki/Largest_remainder_method I need to allocate a trade quantity among 2 or more strategies. e.g. Trade Qty = 99 Strategy A ratio = 0.61 Strategy B ratio = 0.09 Strategy C ratio = 0.23...
  4. M

    Calc II - Disk vs Shell method different volumes

    So I'm getting ready for an exam on tuesday, and I'm using each method for volumes of revolutions for every problem but I'm not getting the same answers. So, let's use this as an example: y = 5x; the shaded region is from [1,2] Using the disk method (about the x-axis) I find: R(x) = 5x; r(x)...
  5. King_Silver

    Question regarding Newton's Method

    So I know how to do Newton's Method without any trouble, taking a value for n then taking it away from the function divided by the derivative of the function I get that entirely and have done roughly 22-23 examples of it over the past 3-4 days. However I have come across one question regarding...
  6. F

    Method of steepest descent for a quartic oscillator

    Homework Statement Homework Equations http://www.maths.manchester.ac.uk/~gajjar/MATH44011/notes/44011_note4.pdf The Attempt at a Solution I obtain i) and ii), but I can't understand the way to study iii) and iv), particularly to choose the rigth paths.[/B]
  7. thegirl

    Method used to find harmonic functions in complex analysis

    Hi, I was just wondering how would you go about finding a harmonic function in complex analysis when given certain conditions such as I am z > 0 and is 1 when x > 0 and 0 when x < 0. Do you draw a diagram? Do you solve the laplace equation? How would you go about doing this? What if there...
  8. davidbenari

    Matrix method to find coefficients of 1-d S.E.

    I haven't taken a course on quantum mechanics yet, but I was asked to solve (numerically) ##[-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}+V(x)]\phi(x)=E\phi(x) ## ##V(x)=2000(x-0.5)^2## by supposing the solution is ##\sum_{0}^{\infty} a_n \phi_n(x)## and ##\phi_n(x)## is the typical solution to the a...
  9. RJLiberator

    Strength/Weakness of Each Method to Collect Earth data

    Homework Statement Name a strength and weakness of each technique. Homework EquationsThe Attempt at a Solution The two techniques that I came up with are: Magnetic Line of Force in rocks to analyze land-based paleomagnetic data. Strength: Well, it's easy to collect. [need help here]...
  10. W

    Solve Truss Joints Using Method of Joints

    Homework Statement Determine the axial forces in the members of the truss and indicate whether they are in tension or compression. Homework Equations Fx = 0 Fy = 0 Mp = 0 The Attempt at a Solution I attempted to find the reactions at the supports first. So: Fx = 0 = Bx + 800cos(250)N Fy...
  11. evinda

    MHB How is the Finite Difference Method Applied in Wave Approximation?

    Hello! (Wave) We consider the finite difference method for the approximation $\left\{\begin{matrix} -u''(x)+q(x)u(x)=f(x)\\ u'(a)=u'(b)=0 \end{matrix}\right.$ and let $K$ be the $(N+2) \times (N+2)$ matrix of the method. Let $v \in \mathbb{R}^{N+2}, v=\begin{pmatrix} v_0\\ v_1\\ \dots\\...
  12. T

    Trying to apply superposition method to circuit, not working

    Homework Statement A double loop circuit is shown in the figure below.[/B] The Emf x = 6.00 V and the Emf w = 19.00 V. Both are shown on the diagram. Calculate the power dissipated in the 6 Ω resistor located on the extreme right in the circuit. Homework Equations V=IR, P=VI The Attempt at...
  13. T

    Runge-Kutta method - Orbital mechanics

    Homework Statement Given: Initial orbital elements of a satellite a=6652.555663km; e=0.075; i=28.5 degrees; Ω=40 degrees; w=30 degrees; n=0 degrees;Tasks(using MATLAB): 1. Convert orbital elements to position and velocity vectors 2. Use these vectors to initialize the Runge-Kutta...
  14. J

    Finding Resultant Force using Component Method

    Homework Statement This is the force table lab that we are doing. F _1 = 300g @ 30^o F _2 = 450g @ 110^o F _3 = 400g @ 230^o F _4 = 270g @ 298^o Finding resultant force using Component Method 1. Express each force F1, F2, and F3 in unit vector notation. Take the origin to be at the center...
  15. R

    Law of multiple proportions (need method check please)

    Homework Statement Homework Equations Law of multiple proportions The Attempt at a Solution Carbon first: 4.61/0.39 = 11.82 C/H Hydrogen 0.39/4.61 = 0.08 H/C therefore 11.82/0.08 = 139.72 ~ 140 masses of carbon that combine with hydrogen are in a 140:1 ratio Does this look right? Or...
  16. ognik

    MHB Learning Lagrange Mesh Method for 1D Schrödinger Eqtn.

    Hi, I have been trying to find some articles that would cover the Lagrange mesh method applied to the 1-D Schrödinger eqtn. - using the Laguerre mesh. I want to develop some fortran programs, for example building Lagrange functions, the kinetic energy matrix elements ... LMM is totally new to...
  17. M

    Undetermined coefficient method

    Homework Statement y''+10y'+25y=x+2+3e-5*x Homework EquationsThe Attempt at a Solution F(D) = D2+10D+25 zeroes: -5 yc= C1*e-5*x + C2*e-5*x *x yp = ax+b + C*e-5*x yp = ax+b + C*e-5*x*x2 I just want to know if my yc and yp is correct, after that I know how to do it.
  18. I

    Finite difference method to solve first-order, multivariable

    I'm trying to replicate the model presented in this [paper](http://www.sciencedirect.com/science/article/pii/S1359431103000474), which is basically to model heat and mass transfer along a one-dimensional duct. There are four characteristic equations for this problem : Momentum conservation...
  19. D

    Determine current and voltage using Node Voltage method

    [Mod note: Post moved to new thread, so template not included] Hello there again! I started working on the second problem but I think I am doing it wrong so I thought I would post the first step and do this one step at a time to see where the mistake was. So the task is to determine UR3 and...
  20. Y

    Solving ODEs with Heun's Method: A Question

    Hi there, in my notes for Heun's method for solving an ODE, I have y(new) = y(old) + 0.5(k1 + k2)Δh And k1 is supposed to be f(y(old)) while k2 is f(y(old) + q11k1Δh) and q11 is 1 So if for example I have a simple differential equation like du/dt = au It would be du/dt = 0.5(k1 + k2) du/dt...
  21. T

    Finding roots using Newton's method in MATLAB

    Homework Statement I am supposed to find the roots of the equation: 10esinx = x2 - 5x +4 in MATLAB using Newton's method with a tolerance of 10-8. There should be three roots. Homework Equations p=po - f(po)/f'(po) |p - po| < TOL The Attempt at a Solution Here is what I have for the code...
  22. evinda

    MHB How to Solve a Boundary Value Problem Using the Finite Difference Method?

    Hello! (Wave) I want to solve numerically the following boundary value problem: $\left\{\begin{matrix} -u''+qu=f & , x \in [a,b]\\ -u'(a)+d_1 u(a)=0 & \\ u'(b)+d_2 u(b)=0 & \end{matrix}\right.$ where $q(x) \geq 0 \forall x \in [a,b], d_1, d_2 \geq 0$. We consider the uniform partition of...
  23. B

    How Do You Compute the Electric Potential Using the Method of Image Charges?

    Hi, I am learning about the method of image charges, but am struggling to sufficiently justify my answer. It appears to be correct, though it quite possibly isn't... 1. Homework Statement (please see attached item) Two semi-infinite grounded conducting planes (the shaded region in the...
  24. Erikono

    Equations of Motion Using Newton's Method --

    Homework Statement Determine the equations of motions in terms of x and gamma. Assume small angles and that the wheel rolls without slip. The mass of the thin homogeneous large disk of radius 2R is 2m. The mass of the thin homogeneous inner disk of radius R is m. The rod of length 2R is...
  25. D

    Looking for online videos on QFT using path integral method

    Hi. I am just starting to study QFT using the path integral method and for which the main textbook is by Srednicki. Does anyone know of any good online videos which would be suitable Thanks
  26. W

    Method for determining error in an equation

    Homework Statement Ok, so suppose I have an equation like V_out = 0.5(1 + R4/R3)(V1+V2) and I know the R3 and R4 has a tolerance of +-5%. For such an equation and similar ones, how would I estimate the possible range of values V_out? For example, I'd like to find out something like...
  27. S

    Method Of Members: Finding reactions

    Homework Statement Dont really need the answer, but I want to know if point C has Cx and Cy or just Cy. I am confused there.
  28. EdajMay

    Truss Analysis : Method of Joints only (Picture provided)

    Hello, In my statics course, we had to design a bridge, and now, I have to calculate the internal forces in every member of the truss. At first, I have found Ay and Oy with the moment of force, but then, I am stuck since the truss is not perfectly aligned. Sadly, I can't use the method of...
  29. Sirsh

    Simple Differentiation - Is this legal / correct method?

    I have the equation: x = 2*L*sin(θ/2) and in my lecture notes they have converted it to: ϑx = L*cos(θ/2)*ϑθ Is it correct to do the following to get this answer? x = 2*L*sin(θ/2) x = 2*L*sin(θ/2)*(ϑ(θ/2)/ϑx) x*ϑx = 2*L*sin(θ/2)*ϑ(θ/2) 1*ϑx = (1/2)*2*L*cos(θ/2)*ϑθ ϑx = L*cos(θ/2)*ϑθ My problem...
  30. Erikono

    Newton's Method for Equations of Motion (Vibrations) help?

    Homework Statement Determine the equations of motions in terms of x and gamma. Assume small angles and that the wheel rolls without slip. The mass of the thin homogeneous large disk of radius 2R is 2m. The mass of the thin homogeneous inner disk of radius R is m. The rod of length 2R is...
  31. mariem.makh

    Fortran FORTRAN Code for Control Volume Finite Element Method Fluid Flow Problems

    where i can found an example A FORTRAN control volume finite element method code FOR FLUID FLOW PROBLEMS thanks for help
  32. davidbenari

    A question related to the method of images and uniqueness theorems

    My question is best illustrated by an example from a Griffiths book on E&M: "A point charge q is situated a distance ##a## from the center of a grounded conducting sphere of radius R (##a>R##). Find the potential outside the sphere... With the addition of a second charge you can simulate any...
  33. mester1025

    Ray tracing with transfer matrix method

    Hi, I'm new in physics and optics so I need a little help. I've a simple optical system from 2 thin lenses. The first thin lens has a focal distance of 50 [mm] , and the second one has 25 [mm]. The 2 lenses are separated by 40 [mm] and the object is placed 75 [mm] before the first lens. I've to...
  34. C

    Atom-Transfer Radical Polymerization: Method Question

    Hi everyone, So I'm a chemical engineering grad student and oddly enough I have been tasked with doing chemistry (strange I know). I'm currently doing atom-transfer radical polymerization (ATRP) using a metal (CuCl or CuBr) and a ligand (dNbpy or PDMETA). My monomer is a methacrylate group...
  35. D

    How Can the Cone Deck Be Mass Produced from Flat Pattern Blanks?

    Hello, I am a last year mechanical engineer student in Marocco, and i have no idea to solve a problem with my final year project, since we have never studied a thing about Metal fabrication. The question is " give one method the Cone Deck could be formed in mass production assuming that flat...
  36. davidbenari

    Two questions related to "classical problem" of the image method

    The classical problem of the image method is: An infinite conducting and grounded (V=0) plate is on the xy plane. A charge ##q## is above it (we can think that it lies on the #z# axis). Knowing that ##V \to 0## as you move far away from the charge and that ##V=0## on the plane find the...
  37. E

    Variation on the Van Der Pauw method

    First time on this forum, hoping you can help clear something up for me. I am using the Van der Pauw method to characterize the sheet resistance of a metal film. In the standard setup, current is pushed through two contacts and voltage is measured across the other two contacts. My colleagues...
  38. TheMathNoob

    Comp Sci Why does this method execute? JAVA

    Homework Statement package myfirstgame; import javax.swing.JFrame; import java.awt.Graphics; /** * * @author danif */ public class MyFirstGame extends JFrame { public MyFirstGame() { setTitle("the game"); setSize(250,250); setResizable(false); setVisible(true)...
  39. N

    Finite Difference Method for non-square grid

    Hi, I have written some codes for the finite difference solution of diffusion equation (\frac{\partial c}{\partial t}= D {\nabla^2 c}, where c is the species concentration and D is the diffusion coefficient) as follows: DO k= 1, tsteps+1 DO i = 2, zsteps DO j = 2, rsteps...
  40. Safinaz

    Question in variational method (QM)

    Homework Statement Hi, in this book " [Nouredine_Zettili]_Quantum_Mechanics_Concepts ", Eq. (9.133) Homework Equations I don't know how the second line had come from the first line:The Attempt at a SolutionI got only two terms such that: $$ < \psi_0| H | \psi_0 > = A^2...
  41. Julio1

    MHB How Do Characteristic Curves Solve This Cauchy Problem?

    Solve the following Cauchy problem using the Method of characteristic curves: $x_1u_{x_1}+x_2u_{x_2}=\alpha u$ in $\mathbb{R}^{+}\times \mathbb{R}^{+}$ $u(x_1,1)=g(x)$ for all $x_1\in \mathbb{R}^{+}.$ Find the local solution for the problem.Hello. I get as solution $g(s)=s$, I want to know if...
  42. J

    Method to distinguish SiO2 and CaCO3

    Homework Statement I chose D, because since SiO2 is an acidic oxide whereas CaCO3 is neutral. But the correct answer is C. And i have doubts on option A and B too.. I can't seem to see why are they not right.. For A, I thought a neutralisarion reaction will happen with SiO2? And for B, I...
  43. J

    Method of Exhuastion for the area of a parabolic segment

    Hello everyone, I'm using the book Apostol- Calculus Vol. 1 for self-studying to get a better understanding of proof based Calculus. They said this book was good for self studying, but I am already stuck in the first chapter. I'm trying to understand how he got the identity: 12+22+...+n(2)=...
  44. Shreyas Shree

    Why does the method of images work?

    Why does the method of images work?
  45. G

    Finding Min. Potential Energy: Variation Calculus Method

    I was solving for a shape on Earth which has minimum potential energy. i used method of variation calculus. I assumed a function f(x) and rotated it around Y axis. sorry for uploading the problem in word.
  46. S

    MHB Using Component Method to Add Vectors

    Use the component method to add the vectors A and B shown in the figure. Both vectors have magnitudes of 3.55 m and vector A makes an angle of $θ = 28.5°$ with the x axis. Express the resultant A + B in unit-vector notation. I don't understand how my answer is wrong. Isn't it $A + B =...
  47. ognik

    MHB Does This ODE Have a Specific Name?

    Hi, thought I had this done, but I get a different answer from my book; I can see where we are different, so would appreciate if someone could tell me what I'm doing wrong here... ODE is $ \d{}{x}[(1-x^2)\d{u}{x}]+\alpha u + \beta x^2u = 0 $, which I rewrote as $ (1-x^2)u'' -2xu' + \alpha u +...
  48. S

    Solving an ODE using shooting method

    Homework Statement I have been trying to solve the following nonlinear ordinary differential equation: ##-\Phi''-\frac{3}{r}\Phi'+\Phi-\frac{3}{2}\Phi^{2}+\frac{\alpha}{2}\Phi^{3}=0## with boundary conditions ##\Phi'(0)=0,\Phi(\infty)=0.##Homework Equations My solution is supposed to...
  49. ChrisVer

    Tight-to-Loose ratio method: QCD Background

    I was reading this document from CMS: https://cds.cern.ch/record/2002036?ln=en But I have some problems understanding how they calculated the bckg coming from the QCD. My questions come from Sec.6 Background, so you can jump and have a quick glimpse over it (?). They used the tight-to-loose...
  50. HollyFlame

    What is Method of Characteristics?

    (I am new to this forum so please do forgive me if I am posting at a wrong place.) Hello, I am a final year student of BS Mechanical Engineering and method of characteristics is not a part of our curriculum. In-fact I heard of it first time after finally picking my FYP. My final year project is...
Back
Top