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Heat Equation Simulation on a 2D Grid

Heat Equation Simulation on a 2D Grid
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2020-01-24 03:29
CalculusDerivativeIntegralProbability & Statistics
This example demonstrates the dynamic behavior of the Heat Equation on a 2D square grid using numerical methods. Key mathematical concepts include partial differential equations, numerical approximation, and heat conduction principles. The construction leverages GeoGebra commands such as Schaltfläche1 (Button1), Time, Schaltfläche2 (Button2), Schaltfläche3 (Button3), dt (time step), Schaltfläche4 (Button4), Schaltfläche5 (Button5), button1, liveUpdateCheckbox, button2, Schaltfläche6, animation_running, Schaltfläche7, λ_T (thermal conductivity), and variables U27 to Z27, N1 to X1 for controlling the simulation and parameters. It is suitable for university students in mathematics or physics, and enthusiasts interested in numerical simulations.

GeoGebra Commands & Parameters

  1. Numeric Time(1)
  2. Numeric dt(0.05)
  3. Boolean liveUpdateCheckbox(true)
  4. false
  5. Numeric λ_T(1)
  6. Numeric U27(NaN)
  7. Numeric N27(NaN)
  8. Numeric O27(NaN)
  9. Numeric P27(NaN)
  10. Numeric Q27(NaN)
  11. Numeric R27(NaN)
  12. Numeric S27(NaN)
  13. Numeric T27(NaN)
  14. Numeric V27(NaN)
  15. Numeric W27(NaN)
  16. Numeric X27(NaN)
  17. Numeric Y27(NaN)
  18. Numeric Z27(NaN)
  19. Numeric N1(NaN)
  20. Numeric O1(NaN)
  21. Numeric P1(NaN)
  22. Numeric Q1(NaN)
  23. Numeric R1(NaN)
  24. Numeric S1(NaN)
  25. Numeric T1(NaN)
  26. Numeric U1(NaN)
  27. Numeric V1(NaN)
  28. Numeric W1(NaN)
  29. Numeric X1(NaN)
  30. Numeric Y1(NaN)
  31. Numeric Z1(NaN)
  32. Numeric N2(NaN)
  33. Numeric O2(NaN)
  34. Numeric P2(NaN)
  35. Numeric Q2(NaN)
  36. Numeric R2(NaN)
  37. Numeric S2(NaN)
  38. Numeric T2(NaN)
  39. Numeric U2(NaN)
  40. Numeric V2(NaN)
  41. Numeric W2(NaN)
  42. Numeric X2(NaN)
  43. Numeric Y2(NaN)
  44. Numeric Z2(NaN)
  45. Numeric N3(NaN)
  46. Numeric O3(NaN)
  47. Numeric P3(NaN)
  48. Numeric Q3(NaN)
  49. Numeric R3(NaN)
  50. Numeric S3(NaN)
  51. Numeric T3(NaN)
  52. Numeric U3(NaN)
  53. Numeric V3(NaN)
  54. Numeric W3(NaN)
  55. Numeric X3(NaN)
  56. Numeric Y3(NaN)
  57. Numeric Z3(NaN)
  58. Numeric N4(NaN)
  59. Numeric O4(NaN)
  60. Numeric P4(NaN)