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. M

    A Example of Ritz method with Bessel functions for trial function

    Hi PF! Do you know of any examples of the Ritz method which use Bessel functions as trial functions? I’ve seen examples with polynomials, Legendre polynomials, Fourier modes. However, all of these are orthogonal with weight 1. Bessel functions are different in this way. Any advice on an...
  2. A

    Can we use the disk method in this integral?

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  3. A

    Problem integrating with the disk method

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  4. D

    AC - Node Voltage Method for difficult circuit

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  5. Celso

    Superposition in separation method of variables

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  6. wrobel

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  7. B

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  8. T

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  9. T

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  10. G

    B Need assistance with an unusual quadratic solution method

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  11. patric44

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  12. Fallen6

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  13. Amrator

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  14. D

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  15. D

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  16. D

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  17. M

    MHB What conditions guarantee convergence of Newton's method for approximating pi/2?

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  18. greg_rack

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  19. jaychay

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  20. jaychay

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  21. jaychay

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  22. jaychay

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  23. jaychay

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  24. I

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  25. B

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  26. O

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  27. H

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  28. hackedagainanda

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  29. C

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  30. A

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  31. J

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  32. J

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  33. Amit1011

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  34. LCSphysicist

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  35. Frigus

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  36. jisbon

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  37. R

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  38. Kaguro

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  39. agnimusayoti

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  40. Leonardo Machado

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  41. L

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  42. Ackbach

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  43. G

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  44. E

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  45. Vick

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  46. ttpp1124

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  47. M

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  48. P

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  49. M

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  50. P

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