What is Method: Definition and 1000 Discussions

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. B

    Comparing Analytic and Approximate Solutions Using Euler's Method in Matlab

    Homework Statement Hello, I am working on a problem involves my using the Euler Method to approximate the differential equation \displaystyle \frac{df}{dt} = af(t) - b[f(t)]^2, both when b=0 and when b is not zero; and I am to compare the analytic solution to the approximate solution when b=0...
  2. MarkFL

    MHB Rico Suave's question at Yahoo Answers regarding using the Gauss-Jordan method

    Here is the question: I have posted a link there to this thread so the OP can view my work.
  3. M

    MHB Implicit finite difference method

    Hey! :o I have a implicit finite difference method for the wave equation. At step 0, we set: $W_j^0=v(x_j), j=0,...,J$ At the step 1, we set: $W_j^1=v(x_j)+Dtu(x_j)+\frac{Dt^2}{2}(\frac{v(x_{j-1})-2v(x_j)+v(x_{j+1})}{h^2}+f(x_j,0)), j=0,...,J$ Can that be that at the step 1 $j$ begins from...
  4. M

    MHB Finite element method for the construction of the approximation of the solution

    Hey! :o Given the following two-point problem: $$-y''(x)+(by)'(x)=f(x), \forall x \in [0,1]$$ $$y(0)=0, y'(1)=my(1)$$ where $ b \in C^1([0,1];R), f \in C([0,1];R)$ and $ m \in R$ a constant. Give a finite element method for the construction of the approximation of the solution $y$ of the...
  5. Mandelbroth

    Formulating a Method of Steepest Ascent on Lie Groups

    Suppose we have a compact Lie group ##G##, and a differentiable function ##f:G_0\to\mathbb{R}## from the identity component of ##G## to the real numbers. I'm looking to maximize the value of this function. Being something of a neophyte at optimization, especially of this kind, I decided to...
  6. P

    Help needed in understanding the author method of solving a DE

    (The full article is here: https://app.box.com/s/bjb63h4nt12rsvdke6yl. The part I would like to ask is on page 995-996)) I am trying to understand the idea behind the author's method in solving the differential equation I'(t) = -D(t) F \big (e^{\int_0^t \theta (u) du} I(t) \big )-...
  7. S

    MHB Two-Phase Method for Solving LPPs Without Art. Vars.

    The following LPP was asked to solve by two phase method Max z=5x+3y subject to 3x+5y<=15 5x+2y<=10 x,y>=0 I have applied Two phase method only in the presence of artificial variables. But in the given problem we need no artificial variable. How to proceed to solve it by two phase method?
  8. S

    MHB Solve LPP with Charnes Big M Method? Wrong Question?

    In a LPP all the constraints are given as 'less than equal to' type. But it was asked to solve the LPP by Charnes Big M method. Is the question wrong? According to me, we have to apply simplex method to solve it. There is no scope tp introduce M.
  9. A

    What are the roles of gas and solid in nanowire growth using the VLS method?

    If you don't know anything about this please just read the first 20 lines on the below link and help me understand (I don't know anything either). The vapour liquid solid method: http://en.wikipedia.org/wiki/Vapor%E2%80%93liquid%E2%80%93solid_method uses a solid, liquid and gas phase to grow...
  10. H

    Moment of Inertia of Hollow Sphere about Center Axis x-y-z method

    Homework Statement Find the moment of inertia of a hollow sphere about a vertical axis through its center in terms of its mass M and radius R. Homework Equations I=\int r^{2} dm The Attempt at a Solution I've been curious about different methods for finding moments of inertia...
  11. H

    The Principle of Fizeau's Method: How a Toothed Wheel Helps Measure Light

    I don't know what is the principle of Fizeau's method. In the experiment a rotating toothed wheel is used.But why the toothed wheel is used? If the toothed wheel is not used,why the time for the light traveled cannot be measured?
  12. S

    MHB Method of Cylindrical Shells (Part 3)

    The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method.. y = -x^2 + 6x - 8, y = 0 so I got -8 to 0 for the integral by plotting the graph... How are they getting 2 to 4? You can't solve that by factoring? And when i...
  13. S

    MHB Method of Cylindrical Shells Question #2

    Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x axis...y = x^3 , y = 8 and x = 0 So my question is: Why did they cube root the y (to be more technical why did they put it in terms of x? I don't...
  14. M

    MHB The finite difference method for the heat equation-error

    Hey! :o I am implementing in a program the finite difference method for the heat equation. The problem is the following: $$u_t(x,t)=(g(x,t)u_x(x,t))_x+f(x,t), \forall (x,t) \in [0,1]x[0,1]$$ $$u(0,t)=u(1,t)=0, \forall t \in [0,1]$$ $$u(x,0)=0, \forall x \in [0,1]$$ where $f(x,t)=\pi x...
  15. P

    Method of characteristics and second order PDE.

    This isn't a homework question per se. Am merely seeking an explanation how the method of characteristics may be applied to a second order PDE. For instance, how is it used to solve utt=uxx-2ut?
  16. B

    Simple Method to Measure Thermal Conductivity of Insulation

    Hi, I'm doing a group investigation on external wall insulation for my school building. The walls do not have a cavity and thus it has been proposed to put insulation over the exterior render of the wall. This is a fairly common building procedure. However, my task is to investigate the...
  17. J

    Using SPICE with FEMM (Finite Element Method Magnetics)

    Hello All, Some of you may have heard of the freeware FEA program called FEMM written by David Meeker. It is used to simulate 2D electromagnetic geometries and also has an integrated LUA scripting host which allows script files to be written to automate the process. I'm currently using...
  18. E

    Implementation of the Numerov Method for the 1D square well

    I want to solve the Schrodinger via the Numerov Method but I had some troubles. I'm programing in C++, so here is my code: #include<cstdlib> #include<iostream> #include<cmath> using namespace std; double x_min=-4.0 , x_max=4.0; int N=2000; double...
  19. C

    Redox reactions oxidation number method

    1) Problem Statement 2) Relevant Equations3) Attempt at Solution For question d, I realize in this case that the substance that is oxidized and reduced is the same molecule : iodine. How do I proceed then as the next step would ask for you to find the change in oxidation numbers and multiplying...
  20. C

    MHB Understanding the Reduction of Order Method for Solving LODEs

    Hi, I'm practicing some of the methods for solving LODE's for my exam tomorrow afternoon and am struggling to understand one of the steps, I'm hoping someone will be able to explain it for me :) So I have the equation $(x-1)y''-xy+y=0$ with x being a solution. Then: $y(x)=xv(t)$...
  21. Ascendant78

    Method for proofs involving vectors and dot products?

    Ok, I'm going to be taking calc III next week, so I wanted to get a head-start by doing the MIT multivariable calculus opencourseware. While most of the material was easy, these proofs are really killing me. Here are two examples: Ex.1: Using vectors and dot product show the diagonals of a...
  22. Q

    Solve GR Equations with Regular Method

    Hi everyone, I don't fully understand what is the regular method to state and solve problems in GR when no handy hints like spherical symmetry or homogeneity of time are assumed. If I find myself in arbitrary reference frame with coordinates x^0, x^1, x^2, x^3 the meaning of which is unknown...
  23. R

    Antisymmetric modeling for panel method solver

    This is a section from the Pan Air user's guide (Pan Air is a aerodynamic panel-method flow solver). I'm confused by the symmetry and anti-symmetry. The first one is easy enough: mirror about the XZ plane (Yimage = -Y, Ximage = X, Zimage = Z). The third one is no symmetry applied. Also easy...
  24. Z

    Fermat Factoring (Zeda's Method)

    Hey everybody, I thought I would share an algorithm for factoring that I designed a few years ago while working on a Z80 project. I noted the same thing Fermat must have: a^{2}-b^{2}=(a+b)(a-b) After a few moments of looking at it, I realized the translation of that simple expression: If I can...
  25. S

    Method of Image grounded conducting sphere.

    Homework Statement A point charge of 10 coulombs is placed at a distance d= 20cm from the centre of an earthed conducting sphere of radius a= 5cm.Find ① The maximum surface density of charge induced on the sphere. ② The force of attraction on the point charge ③ The Sphere is now Insulated...
  26. E

    Frobenius method for fourth order linear ODE

    By using frobenius method I find the roots of the indicial equation of a 4th order ODE to be 0, 1, 1, 2 Now, what is the form of the corresponding series solution of this equation with log terms?
  27. S

    Given f(x) = x^(2/3), find f'(x) using the Δ method.

    Homework Statement Given f(x) = x^(2/3), find f'(x) using the Δ method. Homework Equations f'(x) = (f(x + Δx) – f(x))/(Δx) The Attempt at a Solution I understand the entire solution (that is attached along with the problem as a png file), except how to get [(x + Δx)^(4/3) + (x +...
  28. M

    Runge-Kutta 4 order method. Severe 161: Array bounds exceeded.

    So here I am trying to solve Rayleigh's differential equation using Rungen-Kutta 4th order analytic method. This is what the exercise gives me: X(0 to 40), Y1(0)=0.1, Y2(0)=0, H=0.1, μ=0.5 This is what I ve written and gives me this error: IMPLICIT REAL*8(A-K,O-Z) DIMENSION...
  29. TheFerruccio

    Solve Equation with Method of Frobenius

    Homework Statement Use method of Frobenius to solve this equation: ##y''(x)-y'(x)=x## Homework Equations ------ The Attempt at a Solution Seek an answer of the form ##y=\sum _{n=0}^{\infty } a_n x^{n+r}## Plug into the equation to get... ##\sum _{n=0}^{\infty } a_{n+1} (n+r)...
  30. skyshrimp

    Chloride test question (Mohr's method)

    I'm going to try my first chemistry experiment. http://www.chemteach.ac.nz/investigations/documents/chloride_mohr.pdf I bought 35g of potassium chromate and 5g of silver nitrate. 5g of silver nitrate is only enough for one test. What should I do with the silver afterwards? Is it...
  31. B

    The only method to learn sequences and series

    I remember when I took Calculus B in college. I had never learned any math by reverse engineering before, but when I got to sequences and series, the only way for me to learn how to do it was to reverse engineer it. I had to look up the answer in the back of the textbook, and then work...
  32. S

    Engineering Finding Vo Using Node Voltage Method: A Calculator Puzzle

    Homework Statement Find the voltage Vo using node voltage method specifically.Homework Equations The Attempt at a Solution I am able to get the correct answer when finding the equivalent impedance, then determining the current, and then finding the voltage at the first node V1 by subtrating...
  33. B

    Difficulty manipulating a limit question (secant method)

    Hey, I'm really struggling with this 'show that' question regarding the secant method, I just keep going in circles and I think I may be heading in completely in the wrong direction because I'm not getting anywhere. Homework Statement We're given that, if x* is the zero of f then (we...
  34. M

    Method for checking if digital data is transmitted accurately?

    In this experiment, we recorded a person saying "Aaaaaaa" on the mic as the analog source. And then the analog data was converted into digital data so that the programme in the PC could read it and then the digital data was converted into Analog again to reproduce the recorded voice. I attached...
  35. Einj

    Variational Method and Bound States

    Homework Statement Consider a potential function V(x) such that: $$ \begin{cases} V(x)\leq 0\text{ for }x\in[-x_0,x_0] \\ V(x)=0 \text{ for }x\not\in[-x_0,x_0] \end{cases} $$ Show, using the variational method that: (a) In the 1-dimensional case \lambda^2V(x) always possesses at...
  36. N

    Fourier series: complex vs ordinary method

    Hi! Which is the better method for finding Fourier expansions of a function? The ordinary one (find a_0, b_n and a_n with separate integrals), or the one which uses complex numbers (just find c_n)?
  37. H

    Piston problem -- Method to increase the force against a spring

    Hi people, I need help to this problemSomeone has suggested that the device shown in the figure below be used to improve the maximum force F against the spring, which has a spring constant of k. This is accomplished by changing the temperature of the liquid-vapor mixture in the container. You...
  38. heycoa

    Runge-Kutta Method for a double pendulum

    Hello, I am trying to program a double pendulum via the 4th order Runge-Kutta method and I cannot seem to be getting the right output. At first I used the Euler-Cromer method, but now I am aiming to make it more accurate. Homework Statement I have the equations of motion: d(omega)/dt and...
  39. M

    MHB Jordan Exchange: Exploring the Simplex Method

    Hi! Could you tell me the idea of using Jordan exchange for the Simplex Method?
  40. N

    Can I use method of sections anywhere?

    Homework Statement Find the tension in the rope Homework Equations F=ma The Attempt at a Solution I was wondering whether I could use method of sections in this problem to divide the two systems so that I could find the tension in the rope. I have a strong feeling that I...
  41. R

    MHB Area under a curve using method of exhaustion

    This is a problem from Tom Apostol's calculus book (the very first problem set in the introduction). It wants you to find \int_0^b (ax^m+c)\,dx using Archimedes' method of exhaustion. I'm attaching a diagram and a pdf of my work for the problem since it's rather involved. I'm doing this...
  42. L

    Method to learn electrodynamics?

    Dear friends, can some one tell me the method to learn electrodynamics??(iam a postgraduate student). Thank you
  43. D

    Method of Indicators help

    Homework Statement There are 20 couples who attend a party where there is a raffle. 10 Winners are chosen in the raffle. What is the expected number of couples for which both members win. Homework Equations Assuming method of indicators is used to solve the problem, Ai={members of ith...
  44. F

    Integration of 2 product. possible without numerical method?

    Dear Forum : I hung up with a integration http://ppt.cc/mIpV Can it be deduced to a simpler form? The distribution of σ(E) is http://ppt.cc/-5Z5 The estimation width of x is 10MeV , height is 200mb. The distribution of dE/dx is http://ppt.cc/vcVU Is there a way to do some simple...
  45. B

    Mechanics, acceptable method?

    Homework Statement A ball is dropped from rest from the top of a 6.10m building, falls straight down, collides inelastically with the ground and bounces back. The ball loses 10% of it's K.E every time it hits the ground. How many bounces can happen and the ball still reach a height of 2.44m...
  46. M

    Method of finding natural frequency

    This is a closed loop system. My teacher showed me that one of the methods to find the natural frequency of this system is by finding the frequency at phase -90 degrees. Why must it be -90 degrees? Please explain. From the phase graph, the frequency at -90 degrees is 32 [rad/s], so that's the...
  47. S

    Can this method turn potential energy into kinetic energy?

    I am wondering if this method is in use already somewhere, or if its possible to be used. For example, using the equation of gravitational potential energy a 100kg weight that freefalls 100 meters has 98,000 J of energy, which equals 24,000 watts after approx 4 seconds of freefall. Assuming I...
  48. A

    Understanding Gauss-Jordan Method for Solving Equations

    can someone explain me in detail or simply how Gauss-Jordan way of solving equations works? thanks.
  49. MarkFL

    MHB しおり's question at Yahoo Answers regarding Newton's method

    Here is the question: I have posted a link there to this thread so the OP can see my work.
  50. S

    Critiquing separation of variables method for PDE.

    "Critiquing" separation of variables method for PDE. I am currently taking a course in PDE's and it has been very "applied" and not so much theory based. I can say its been separate this separate that separate this separate that… Enough! We are always "separating variables" and it always...
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