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Euler's Method

Euler's Method
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2019-08-19 13:21
FunctionSequenceCalculus
In collections SCIE1000
This example demonstrates Euler's method, a numerical technique for solving differential equations. It iteratively calculates to approximate the solution of a differential equation. The example uses GeoGebra commands such as Sequence, PolyLine, and Textfield to show how to approach the solution by setting initial conditions and step size. Suitable for high school math education and students learning differential equations.

GeoGebra Commands & Parameters

  1. Sequence((Element[xns, i], Element[yns, i]), i, 1, 300) → pointsxyns
  2. PolyLine(pointsxyns) → f
  3. Sequence(Element[xns, i], i, 1 + n, 11 + n) → list1
  4. Sequence(Element[yns, i], i, 1 + n, 11 + n) → list2
  5. Sequence(i, i, n, n + 10) → list3
  6. Element(list3, D1) → E1
  7. Element(list3, D2) → E2
  8. Element(list3, D3) → E3
  9. Element(list3, D4) → E4
  10. Element(list3, D5) → E5
  11. Element(list3, D6) → E6
  12. Element(list3, D7) → E7
  13. Element(list3, D8) → E8
  14. Element(list3, D9) → E9
  15. Element(list3, D10) → E10
  16. Element(list3, D11) → E11
  17. Element(list1, D1) → F1
  18. Element(list1, D2) → F2
  19. Element(list1, D3) → F3
  20. Element(list1, D4) → F4
  21. Element(list1, D5) → F5
  22. Element(list1, D6) → F6
  23. Element(list1, D7) → F7
  24. Element(list1, D8) → F8
  25. Element(list1, D9) → F9
  26. Element(list1, D10) → F10
  27. Element(list1, D11) → F11
  28. Element(list2, D1) → G1
  29. Element(list2, D2) → G2
  30. Element(list2, D3) → G3
  31. Element(list2, D4) → G4
  32. Element(list2, D5) → G5
  33. Element(list2, D6) → G6
  34. Element(list2, D7) → G7
  35. Element(list2, D8) → G8
  36. Element(list2, D9) → G9
  37. Element(list2, D10) → G10
  38. Element(list2, D11) → G11
  39. Textfield(Ax) → InputBox1
  40. Textfield(Ay) → InputBox2
  41. Textfield(F) → InputBox3
  42. Textfield(h) → InputBox4
  43. Min(list1) → xmin
  44. Max(list1) → xmax
  45. Min(list2) → ymin
  46. Max(list2) → ymax
  47. If(h ≥ 1.5, 0.7, If[1 < h < 1.5, 0.5, If[0.2 < h ≤ 1, 0.2, 0.1]]) → posx
  48. Sequence(Text["y_{" + (i) + "}", (x(Element[pointsxyns, i + 1]) + posx, y(Element[pointsxyns, i + 1]))], i, 1, 40) → Labels
  49. TableText({{"n", "x_n", "y_n"}, {E1, F1, G1}, {E2, F2, G2}, {E3, F3, G3}, {E4, F4, G4}, {E5, F5, G5}, {E6, F6, G6}, {E7, F7, G7}, {E8, F8, G8}, {E9, F9, G9}, {E10, F10, G10}, {E11, F11, G11}}, "|_") → text1
  50. SolveODE(F, x(A), y(A), 120, 0.01) → numericalIntegral1