Method Definition and 14 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. D

    Euler Method in C++

    Summary: Problem with Euler Method in C++ Hello, I have a very difficult problem for me (a beginner in programming) how to make the version of the euler method presented in c ++ with the void, float functions, so that the program will calculate from the data that I enter during the program...
  2. H

    How can I calculate the number of photons with this data?

    The problem says: A radio station emits electromagnetic wave with a frequency of 100MHz (102*106 Hz). a)What's the energy of this radiation's/glow's photon? (Solved, i found 6,63*10-26 J) b)Compare your calculation with the energy of another visible radiation/glow, with a wavelength of 600nm...
  3. donaldparida

    B Methods of integration: direct and indirect substitution

    I have seen two approaches to the method of integration by substitution (in two different books). On searching the internet i came to know that Approach I is known as the method of integration by direct substitution whereas Approach II is known as the method of integration by indirect...
  4. S

    Operational State of a Bulb

    What methods other than Light Dependent Resistor incorporation are there to determine the 'bulb state'? I'm guessing it's going to include the use of another type of optoelectric component? Thanks
  5. W

    Complex Solutions to Oscillations

    Homework Statement Homework Equations The Attempt at a Solution I tried differentiating both sides of 3 and re-arranging it such that it started to look like equation 2, however i got stuck with 2 first order terms z' and couldn't find a way to manipulate it into a function z. I then...
  6. S

    MATLAB Separation of variables in MATLAB

    Hello, I haven't found any program that can be used to perform separation of variables on difficult PDEs. Is there such a method somewhere?
  7. Rocky_Tseng

    Intro Physics Is there a book about how to do research in Physics?

    Is there a book about how to do research in Physics or Physicist's experience? especially in Astrophysics, if not, general physics is also very good. thanks.
  8. S

    Root-Finding method in MATLAB

    Homework Statement Compute and plot the compressibility factor (y) verses pressure (x) for the (1) Van der Waal’s (2) Redlich-Kwong and (3) Peng-Robinson equations of state. Compressibility Factor, Z = (P*v)/(R*T); where v is the specific volume (V/v). Data for n-Butane: T = 500 K; Tc = 425.2...
  9. 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...
  10. Y

    Finding the maximum value of a function

    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...
  11. 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)...
  12. Y

    Heun's method 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...
  13. B

    Abaqus 6.14 CAE - Imperfection Study

    The title of the project is as follows: A study of the effect of imperfections on the buckling capability of a soda can under axial loading. My group and I are aiming to carry out the following: Linear buckling analysis of soda can to gain first 5 eigenvalues Riks buckling analysis with...
  14. S

    Frobenius method for Hermite Equation

    Homework Statement I'm asked to solve the Hermite Differential Equation y''(x) - 2 x y'(x) + \lambda y(x) = 0 using the Frobenius method 2. Homework Equations I am to assume the solution is in the form y(x) = \sum a_n x^{n+r} where r are the roots of the indicial equation that in this...