1. Numerical Solution for Initial Value Problem Numerical Analysis

2. Introduction x0x0 x1x1 x2x2 x3x3 xnxn

3. Well-posed Problem

4. Well-posed Formula: Example

5. Classes of Methods

7. Euler Method

9. Euler Method: Formula

10. Euler Method: Geometry Meaning

11. Euler Method: Example

13. Taylor order n

14. Taylor order n: Formula

15. Taylor order n: Example

22. Interpolate other values

25. Runge-Kutta Method (RK) Runge-Kutta 25

26. Taylor Theory in 2 Variables 26

27. Runge-Kutta order 2 27

28. Runge-Kutta order 2 28

29. Runge-Kutta order 2 29

30. Runge-Kutta order 2 30

31. RK2: Midpoint Formula 31

32. RK2: Modified Euler Formula 32

33. RK2: Heuns Formula 33

34. RK2: Example 34

35. RK2: Example 35

36. RK2: Example 36

37. RK2: Example 37

38. RK2: Example 38

39. Runge-Kutta order 4 39

40. RK4: Example 40

41. RK4: Example 41

42. RK4: Example 42

43. RK4: Example 43

44. RK4: Example 44

45. RK4 vs Other Methods 45

46. RK4 vs Other Methods 46

47. RK4 vs Other Methods 47

48. Multi-Step Method 48

49. Multi-Step Method 49

50. Multi-Step Method: Explicit case 50

51. Adams-Bashforth Formula 51

52. Multi-Step Method: Explicit case 52

53. Multi-Step Method: Explicit case 53

54. Multi-Step Method: Implicit case 54

55. Multi-Step Method: Implicit case 55

56. Predictor-Corrector Method 2 (Predictor Formula) (Corrector Formula) (inner iteration) 56

57. Predictor-Corrector Method 57

58. Predictor-Corrector Method 58

59. Predictor-Corrector Method: Example 59

60. Predictor-Corrector Method: Example 60

61. Predictor-Corrector Method: Example 61

62. Predictor-Corrector Method: Example 62

63. Predictor-Corrector Method: Example 63

64. High ODE and System of ODE

68. RK4 in vector form

69. ABM4 in vector form

70. High ODE and System of ODE: Example

79. Divided Different Method for BVP

80. Differential Equation to Divided Different Form

81. Divided Different Formula for Linear BVP

82. Existing of Solution

83. Divided Different for BVP: Example