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. P

    MHB Hayldiburasomas' question via email about Secant Method

    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{...
  2. P

    MHB Alexander's question via email about Newton's Method

    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?
  3. P

    MHB Lachlan's question via email about the Bisection Method

    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} $...
  4. Leonardo Machado

    A Rational Chebyshev Collocation Method For Damped Harmonic Oscilator

    Hello everyone. I'm currently trying to solve the damped harmonic oscillator with a pseudospectral method using a Rational Chebyshev basis $$ \frac{d^2x}{dt^2}+3\frac{dx}{dt}+x=0, \\ x(t)=\sum_{n=0}^N TL_n(t), \\ x(0)=3, \\ \frac{dx}{dt}=0. $$ I'm using for reference the book "Chebyshev and...
  5. J

    MHB Minimum Degree of a Random Graph (Probabilistic Method)

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  6. bagasme

    B Derivation of Cosine and Sine Method of Vector Sum

    Hello all, In high school physics, the magnitude sum of vector addition can be found by cosine rule: $$\vec {R^2} = \vec {F^2_1} + \vec {F^2_2} + 2 \cdot \vec F_1 \cdot \vec F_2 \cdot cos ~ \alpha$$ and its angle are calculated by sine rule: $$\frac {\vec R} {sin ~ \alpha} = \frac {\vec F_1}...
  7. Eclair_de_XII

    B Is this method of estimating Pi too similar to Archimedes' method?

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  8. R

    Misc. Mechanism or method to unlock a window from the outside?

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  9. L

    Finite difference method for the diffusion-advection equation

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  10. V

    Is My Python Bisection Method Code Correct?

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  11. H

    I The irreducible representations of of su(2): Highest weight method

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  12. T

    Quick Method of Calculating the 2nd Moment Of Area Of an I Beam

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  13. M

    Stiffness Matrix Method: Symmetry vs Introducing a new node / joint

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  14. T

    Abuse of the Finite Element Method

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  15. C

    Trapezoid method converges faster than the Simpson method

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  16. C

    Doubts about the method of determining the elastic constant of a spring

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  17. Sabra_a

    When to use the Lumped Capacitance method in Heat Transfer problems?

    I attached below my attempt to solve the question.
  18. C

    I Does the Euler method give a better insight into adiabatic processess?

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  19. E

    Not sure why my method doesn't work: Springs, Potential Energy and Work

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  20. JD_PM

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  21. A

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  22. J

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  23. Anonymous_

    I What is the most useful method to solve differential equations?

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  24. Purahei

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  25. C

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  26. ExplosivePete

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  27. B

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  28. T

    What do the numbers in the method of joints analysis for trusses represent?

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  29. jisbon

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  30. N

    How to judge the singularity of a matrix in numerical method?

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  31. R

    Experimental method question - electrochemistry

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  32. H

    A Crank-Nicholson method and Robin boundary conditions

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  33. karush

    MHB 2.2.294 Euler's method word problem

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  34. karush

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  35. Huyanyinglei

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  36. Another

    What is the Savitzky-Golay 2nd derivative method?

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  37. Arman777

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  38. S

    [E&M] Question on the Image charge method of a grounding sphere

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  39. sdefresco

    3-D Planar Method of Images Boundary Problem

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  40. S

    Lill's method for solving polynomial equations

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  41. e101101

    Energy Method: Inclined Plane - Solving for Velocity and Time

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  42. G

    Any plausible non-rocket based method to reach orbit?

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  43. X

    Cube root long division method

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  44. X

    I Challenges to the Redshift Method and Hubble's Law

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  45. TytoAlba95

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  46. D

    I What Is the Best Numerical Method for Solving a PDE on a 2D Annulus Grid?

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  47. Abhimessi10

    Engineering Houston's piezoelectric method for finding the velocity of light

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  48. JD_PM

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  49. Graeme M

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  50. G

    How to use the Double integration method for an overhanging beam?

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