Numerical Methods & Analysis

ืžื›ื™ืœ ืžื•ื“ืขื•ืช
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ื”ื•ืจื“ื•ืช
ืกื™ื•ื•ื’ ืชื•ื›ืŸ
ื›ื•ืœื
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš

ืžื™ื“ืข ืขืœ ื”ืืคืœื™ืงืฆื™ื” ื”ื–ื•

ืฉื™ื˜ื•ืช ืžืกืคืจื™ื•ืช:

ื”ืืคืœื™ืงืฆื™ื” ื”ื™ื ืžื“ืจื™ืš ื—ื™ื ืžื™ ืžืœื ืฉืœ ืฉื™ื˜ื•ืช ื•ื ื™ืชื•ื— ืžืกืคืจื™ื™ื ื”ืžื›ืกื” ื ื•ืฉืื™ื ื—ืฉื•ื‘ื™ื, ื”ืขืจื•ืช ื•ื—ื•ืžืจื™ื ื‘ืงื•ืจืก.

ืืคืœื™ืงืฆื™ื” ื–ื• ืžืคืจื˜ืช 77 ื ื•ืฉืื™ื ืขื ื”ืขืจื•ืช ืžืคื•ืจื˜ื•ืช, ื“ื™ืื’ืจืžื•ืช, ืžืฉื•ื•ืื•ืช, ื ื•ืกื—ืื•ืช ื•ื—ื•ืžืจ ืงื•ืจืก, ื”ื ื•ืฉืื™ื ืžืคื•ืจื˜ื™ื ื‘-5 ืคืจืงื™ื. ื”ืืคืœื™ืงืฆื™ื” ื—ื™ื™ื‘ืช ืœื”ื™ื•ืช ืœื›ืœ ื”ืกื˜ื•ื“ื ื˜ื™ื ื•ื”ืžืงืฆื•ืขื ื™ื ื‘ืžื“ืขื™ ื”ื”ื ื“ืกื”.

ื”ื•ืจื“ ืืช ื”ืืคืœื™ืงืฆื™ื” ื›ื—ื•ืžืจ ืขื–ืจ ื•ืกืคืจ ื“ื™ื’ื™ื˜ืœื™ ืขื‘ื•ืจ ืชื•ื›ื ื™ื•ืช ืžืชืžื˜ื™ืงื” ื•ื”ื ื“ืกืช ืžื›ื•ื ื•ืช ื•ืงื•ืจืกื™ื ืœืชื•ืืจ. ื”ืžื—ืงืจ ื ืžืฆื ื‘ืฉื™ืžื•ืฉ ื ืจื—ื‘ ื’ื ื‘ื‘ื™ื ื” ืžืœืื›ื•ืชื™ืช, ืืœื’ื•ืจื™ืชืžื™ื, ืžืขืจื›ื•ืช ื–ืžืŸ ืืžืช ื•ืœืžื™ื“ืช ืžื›ื•ื ื”.

ื”ืืคืœื™ืงืฆื™ื” ืžื™ื•ืขื“ืช ืœืœืžื™ื“ื” ืžื”ื™ืจื”, ืชื™ืงื•ื ื™ื, ื”ืคื ื™ื•ืช ื‘ื–ืžืŸ ืžื‘ื—ื ื™ื ื•ืจืื™ื•ื ื•ืช.

ืืคืœื™ืงืฆื™ื” ื–ื• ืžื›ืกื” ืืช ืจื•ื‘ ื”ื ื•ืฉืื™ื ื”ืงืฉื•ืจื™ื ื•ื”ืกื‘ืจ ืžืคื•ืจื˜ ืขื ื›ืœ ื”ื ื•ืฉืื™ื ื”ื‘ืกื™ืกื™ื™ื.

ื—ืœืง ืžื”ื ื•ืฉืื™ื ื”ืžื›ื•ืกื™ื ื‘ื™ื™ืฉื•ื ื–ื” ื”ื:

1. ืคืชืจื•ืŸ ืžืฉื•ื•ืื•ืช ืืœื’ื‘ืจื™ื•ืช ื•ื˜ืจื ืกืฆื ื“ื ื˜ืœื™ื•ืช
2. ืฉื™ื˜ื•ืช ืœืคืชืจื•ืŸ ืฉื•ืจืฉื™ื ืฉืœ ืžืฉื•ื•ืื•ืช ืคื•ืœื™ื ื•ืžื™ื•ืช
3. ืงื™ืจื•ื‘ ืจืืฉื•ื ื™ ืœื”ืœื™ืš ืื™ื˜ืจื˜ื™ื‘ื™
4. ืฉื™ื˜ืช ืžื™ืงื•ื ื›ื•ื–ื‘
5. ืฉื™ื˜ืช ื ื™ื•ื˜ื•ืŸ ืจืคืกื•ืŸ
6. ืฉื™ื˜ืช ืื™ื˜ืจืฆื™ื” ื›ืœืœื™ืช
7. ื”ืชื›ื ืกื•ืช ืฉื™ื˜ื•ืช ื”ืื™ื˜ืจืฆื™ื”
8. ืžืขืจื›ืช ืœื™ื ืืจื™ืช ืฉืœ ืžืฉื•ื•ืื•ืช ืืœื’ื‘ืจื™ื•ืช
9. ืฉื™ื˜ื” ื™ืฉื™ืจื” ืœืคืชืจื•ืŸ ืžืขืจื›ืช ืœื™ื ืืจื™ืช
10. ืฉื™ื˜ืช ื—ื™ืกื•ืœ Guass
11. ืฉื™ื˜ืช Guass Jordan
12. ืฉื™ื˜ื•ืช ืื™ื˜ืจื˜ื™ื‘ื™ื•ืช
13. ืฉื™ื˜ืช ืื™ื˜ืจืฆื™ื” ื’ืื•ืก-ื™ืขืงื•ื‘ื™
14. ืฉื™ื˜ืช ืื™ื˜ืจืฆื™ื” ื’ืื•ืก-ื–ื™ื™ื“ืœ
15. ื‘ืขื™ื•ืช ืขืจืš ืขืฆืžื™
16. ืฉื™ื˜ืช ื›ื•ื—
17. ืื™ื ื˜ืจืคื•ืœืฆื™ื”
18. ืื™ื ื˜ืจืคื•ืœืฆื™ื” ืœื’ืจื ื–'
19. ืื™ื ื˜ืจืคื•ืœืฆื™ื” ืœื™ื ืืจื™ืช
20. ืื™ื ื˜ืจืคื•ืœืฆื™ื” ืจื™ื‘ื•ืขื™ืช
21. ืฉื’ื™ืื” ืฉืœ ืื™ื ื˜ืจืคื•ืœืฆื™ื”
22. ื”ื‘ื“ืœื™ื ืžื—ื•ืœืงื™ื
23. ืื™ื ื˜ืจืคื•ืœืฆื™ื” ืžื—ื•ืœืงืช ืฉืœ ื ื™ื•ื˜ื•ืŸ
24. ืื™ื ื˜ืจืคื•ืœืฆื™ื” ืขื ื ืงื•ื“ื•ืช ืžืจื•ื•ื—ื•ืช ื‘ืื•ืคืŸ ืฉื•ื•ื”
25. ืงืฉืจื™ื ื‘ื™ืŸ ื”ื‘ื“ืœื™ื ืœื ื’ื–ืจื•ืช
26. ื ื•ืกื—ืช ื”ื‘ื“ืœ ืงื“ื™ืžื” ืฉืœ ื ื™ื•ื˜ื•ืŸ
27. ื ื•ืกื—ืช ืื™ื ื˜ืจืคื•ืœืฆื™ื” ืœืื—ื•ืจ ืฉืœ ื ื™ื•ื˜ื•ืŸ
28. ืคื•ื ืงืฆื™ื™ืช Spline
29. ืื™ื ื˜ืจืคื•ืœืฆื™ื” ืžืขื•ืงื‘ืช
30. ื‘ื™ื“ื•ืœ ืžืกืคืจื™
31. ื ื’ื–ืจื™ื ื‘ืืžืฆืขื•ืช ื ื•ืกื—ืช ื”ื‘ื“ืœ ืงื“ื™ืžื” ืฉืœ ื ื™ื•ื˜ื•ืŸ
32. ื ื’ื–ืจื•ืช ื‘ืืžืฆืขื•ืช ื ื•ืกื—ืช ื”ื”ืคืจืฉ ืœืื—ื•ืจ ืฉืœ ื ื™ื•ื˜ื•ืŸ
33. ื ื’ื–ืจื™ื ื‘ืืžืฆืขื•ืช ื ื•ืกื—ืช ื”ืคืจืฉ ืžื—ื•ืœืง
34. ื›ืœืœื™ ืื™ื ื˜ื’ืจืฆื™ื” ื•ืื™ื ื˜ื’ืจืฆื™ื” ืžืกืคืจื™ื™ื ื”ืžื‘ื•ืกืกื™ื ืขืœ ืžืจื•ื•ื— ืจืฉืช ืื—ื™ื“
35. ื›ืœืœ ื”ื˜ืจืคื–
36. ืฉื’ื™ืื” ื‘ื›ืœืœ ื”ื˜ืจืคื–
37. ื›ืœืœ ื˜ืจืคื– ืžื•ืจื›ื‘
38. ื—ื•ืง 1/3 ืฉืœ ืกื™ืžืคืกื•ืŸ
39. ื˜ืขื•ืช ื‘ื›ืœืœ 1/3 ืฉืœ ืกื™ืžืคืกื•ืŸ
40. ื—ื•ืง 1/3 ืฉืœ ืกื™ืžืคืกื•ืŸ ืžื•ืจื›ื‘
41. ื—ื•ืง 3/8 ืฉืœ ืกื™ืžืคืกื•ื
42. ืฉื™ื˜ืช ืจื•ืžื‘ืจื’
43. ืฉื™ื˜ืช ืจื•ืžื‘ืจื’ ืœื›ืœืœ ื”ื˜ืจืคื–
44. ืฉื™ื˜ืช ืจื•ืžื‘ืจื’ ืœื—ื•ืง 1/3 ืฉืœ ืกื™ืžืคืกื•ืŸ
45. ื›ืœืœื™ ืฉื™ืœื•ื‘ ื’ืื•ืก-ืœื’ื ื“ืจื”
46. โ€‹โ€‹ื›ืœืœ ื ืงื•ื“ื” ืื—ืช ืฉืœ ื’ืื•ืก (ื›ืœืœ ื ืงื•ื“ื” ืื—ืช ืฉืœ ื’ืื•ืก-ืœื’ื ื“ืจ)
47. ื›ืœืœ ืฉืชื™ ื ืงื•ื“ื•ืช ืฉืœ ื’ืื•ืก (ื—ื•ืง ืฉืชื™ ื ืงื•ื“ื•ืช ืฉืœ ื’ืื•ืก-ืœื’ื ื“ืจ)
48. ื—ื•ืง ืฉืœื•ืฉ ื ืงื•ื“ื•ืช ื’ืื•ืก (ื—ื•ืง ืฉืœื•ืฉ ื ืงื•ื“ื•ืช ื’ืื•ืก-ืœื’ื ื“ืจ)
49. ื”ืขืจื›ืช ืื™ื ื˜ืจื’ืจืœ ื›ืคื•ืœ ื‘ืืžืฆืขื•ืช ื›ืœืœ ื˜ืจืคื–
50. ื”ืขืจื›ื” ืฉืœ ืื™ื ื˜ืจื’ืจืœ ื›ืคื•ืœ ื‘ืืžืฆืขื•ืช ื”ื›ืœืœ ืฉืœ ืกื™ืžืคืกื•ืŸ
51. ืžื‘ื•ื ืœื‘ืขื™ื™ืช ืขืจืš ืจืืฉื•ื ื™ ืขื‘ื•ืจ ืžืฉื•ื•ืื•ืช ื“ื™ืคืจื ืฆื™ืืœื™ื•ืช ืจื’ื™ืœื•ืช
52. ื”ืคื—ืชืช ืžืฉื•ื•ืืช ืžืกื“ืจ ืฉื ื™ ืœืžืขืจื›ืช ืžืกื“ืจ ืจืืฉื•ืŸ
53. ืฉื™ื˜ืช ืฆืขื“ ื‘ื•ื“ื“
54. ืฉื™ื˜ื•ืช ืžืจื•ื‘ื•ืช ืฉืœื‘ื™ื
55. ืฉื™ื˜ืช ืกื“ืจืช ื˜ื™ื™ืœื•ืจ
56. ืฉื™ื ื” ืืช ืฉื™ื˜ื•ืช ืื•ื™ืœืจ ืื• ื”ื•ืŸ
57. ืฉื™ื˜ื•ืช ืจื•ื ื’ ืงื•ื˜ื”

ื›ืœ ื ื•ืฉื ืฉืœื ืขื ื“ื™ืื’ืจืžื•ืช, ืžืฉื•ื•ืื•ืช ื•ืฆื•ืจื•ืช ืื—ืจื•ืช ืฉืœ ื™ื™ืฆื•ื’ื™ื ื’ืจืคื™ื™ื ืœืœืžื™ื“ื” ื˜ื•ื‘ื” ื™ื•ืชืจ ื•ื”ื‘ื ื” ืžื”ื™ืจื”.

ื›ืœ ื”ื ื•ืฉืื™ื ืื™ื ื ืจืฉื•ืžื™ื ื‘ื’ืœืœ ืžื’ื‘ืœื•ืช ืื•ืคื™.

ืžืืคื™ื™ื ื™ื :
* ื ื•ืฉืื™ื ืฉืœืžื™ื ืžื‘ื—ื™ื ืช ืคืจืง
* ืคืจื™ืกืช ืžืžืฉืง ืžืฉืชืžืฉ ืขืฉื™ืจื”
* ืžืฆื‘ ืงืจื™ืื” ื ื•ื—
* ื ื•ืฉืื™ ื‘ื—ื™ื ื” ื—ืฉื•ื‘ื™ื
* ืžืžืฉืง ืžืฉืชืžืฉ ืคืฉื•ื˜ ืžืื•ื“
* ืžื›ืกื” ืืช ืจื•ื‘ ื”ื ื•ืฉืื™ื
* ืงืœื™ืง ืื—ื“ ืงื‘ืœ ืงืฉื•ืจ ื›ืœ ื”ืกืคืจ
* ืชื•ื›ืŸ ืžื•ืชืื ืœื ื™ื™ื“
* ืชืžื•ื ื•ืช ืžื•ืชืืžื•ืช ืœื ื™ื™ื“

ืืคืœื™ืงืฆื™ื” ื–ื• ืชื”ื™ื” ืฉื™ืžื•ืฉื™ืช ืœืขื™ื•ืŸ ืžื”ื™ืจ. ื ื™ืชืŸ ืœืกื™ื™ื ืืช ื”ืขื“ื›ื•ืŸ ืฉืœ ื›ืœ ื”ืžื•ืฉื’ื™ื ืชื•ืš ืžืกืคืจ ืฉืขื•ืช ื‘ืืžืฆืขื•ืช ื”ืืคืœื™ืงืฆื™ื” ื”ื–ื•.

ืฉื™ื˜ื•ืช ื•ื ื™ืชื•ื— ืžืกืคืจื™ื™ื ื”ื ื—ืœืง ืžืงื•ืจืกื™ ื—ื™ื ื•ืš ืœืžืชืžื˜ื™ืงื” ื•ื”ื ื“ืกืช ืžื›ื•ื ื•ืช ื•ืชื›ื ื™ื•ืช ืœืชื•ืืจ ื˜ื›ื ื•ืœื•ื’ื™ ืฉืœ ืื•ื ื™ื‘ืจืกื™ื˜ืื•ืช ืฉื•ื ื•ืช.

ื‘ืžืงื•ื ืœืชืช ืœื ื• ื“ื™ืจื•ื’ ื ืžื•ืš ื™ื•ืชืจ, ืื ื ืฉืœื— ืœื ื• ืืช ื”ืฉืื™ืœืชื•ืช, ื”ื‘ืขื™ื•ืช ืฉืœืš ื•ืชืŸ ืœื ื• ื“ื™ืจื•ื’ ื•ื”ืฆืขื” ื—ืฉื•ื‘ื™ื ื›ื“ื™ ืฉื ื•ื›ืœ ืœืฉืงื•ืœ ื–ืืช ืขื‘ื•ืจ ืขื“ื›ื•ื ื™ื ืขืชื™ื“ื™ื™ื. ื ืฉืžื— ืœืคืชื•ืจ ืœื›ื ืื•ืชื.
ืขื“ื›ื•ืŸ ืื—ืจื•ืŸ ื‘ืชืืจื™ืš
25 ื‘ืื•ื’ืณ 2025

ืื‘ื˜ื—ืช ื ืชื•ื ื™ื

ื›ื“ื™ ืœืฉืžื•ืจ ืขืœ ื”ื‘ื˜ื™ื—ื•ืช ืฆืจื™ืš ืงื•ื“ื ื›ืœ ืœื”ื‘ื™ืŸ ืื™ืš ื”ืžืคืชื—ื™ื ืื•ืกืคื™ื ื•ืžืฉืชืคื™ื ืืช ื”ื ืชื•ื ื™ื ืฉืœืš. ื ื•ื”ืœื™ ืคืจื˜ื™ื•ืช ื”ื ืชื•ื ื™ื ื•ืื‘ื˜ื—ืช ื”ื ืชื•ื ื™ื ืขืฉื•ื™ื™ื ืœื”ืฉืชื ื•ืช ื‘ื”ืชืื ืœืฉื™ืžื•ืฉ, ืœืื–ื•ืจ ื•ืœื’ื™ืœ ื”ืžืฉืชืžืฉ. ื”ืžืคืชื— ืกื™ืคืง ืืช ื”ืžื™ื“ืข ื”ื–ื” ื•ื”ื•ื ืขืฉื•ื™ ืœืขื“ื›ืŸ ืื•ืชื• ืžื“ื™ ืคืขื.
ืœื ืžืชื‘ืฆืข ืฉื™ืชื•ืฃ ื ืชื•ื ื™ื ืขื ืฆื“ื“ื™ื ืฉืœื™ืฉื™ื™ื
ื”ื ืชื•ื ื™ื ืžื•ืฆืคื ื™ื ื‘ื–ืžืŸ ื”ื”ืขื‘ืจื”
ืื™ ืืคืฉืจ ืœืžื—ื•ืง ืืช ื”ื ืชื•ื ื™ื

ืชืžื™ื›ื” ื‘ืืคืœื™ืงืฆื™ื”

ืžื™ื“ืข ืขืœ ืžืคืชื—ื™ ื”ืืคืœื™ืงืฆื™ื”
Bhanuben B. Thummar
georgydoki@gmail.com
India
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