Numerical Analysis

Abdullah Mijazi

Iqukethe izikhangiso

Mayelana nalolu hlelo lokusebenza

Lolu hlelo lokusebenza akuyona nje wokubala; kunalokho ikhiqiza izixazululo ezinemininingwane yesinyathelo ngesinyathelo zezinkinga zisebenzisa izindlela ezahlukahlukene ezaziwayo. Kusiza kakhulu ukuqonda inqubo yezindlela ezahlukene kanye nokuthola nokulungisa amaphutha ezibalweni ezinde.

Lolu hlelo lokusebenza lwakha ifomula ngendlela eguquguqukayo ngokuya ngenkinga ethile, bese lufaka amanani kuleyo fomula ngesikhathi sangempela, bese lubala, ukuze umphumela walo wokugcina ubukeke sengathi kukhona umuntu obhale zonke izibalo ngepeni nangephepha.

Lolu hlelo lokusebenza lukhiqiza izixazululo ezinemininingwane yesinyathelo ngesinyathelo ngezindlela ezilandelayo.

1. Ukuhunyushwa Kwezinombolo

a) Isikhawu Esigxilile
i. I-Newton Forward Interpolation.
ii. I-Newton Backward Interpolation.
iii. I-Gauss Forward Interpolation.
iv. I-Gauss Backward Interpolation.
v. I-Stirling Interpolation.
vi. I-Bessel Interpolation.
vii. I-Everett Interpolation.
viii. I-Lagrange Interpolation.
ix. I-Aitken Interpolation.
x. I-Newton Divided Difference Interpolation.

b) Isikhawu Esiguquguqukayo
i. I-Lagrange Interpolation.
ii. I-Aitken Interpolation.
iii. I-Newton Divided Difference Interpolation.

2. Umehluko Wezinombolo
a) Newton Forward Differentiation.
b) Newton Backward Differentiation.
c) Ukuhlukanisa umehluko.
d) I-Bessel Differentiation.
e) Everett Differentiation.
f) I-Gauss Forward Differentiation.
g) Umehluko Osemuva we-Gauss.

3. Ukuhlanganiswa Kwezinombolo
a) Ukudidiyelwa koMthetho Ophakathi.
b) Ukuhlanganiswa Komthetho We-Trapezoidal.
c) I-Simpson's 1/3 Rule Integration.
d) I-Simpson's 3/8 Rule Integration.
e) Ukuhlanganiswa Komthetho We-Boole.
f) Ukuhlanganiswa Kwemithetho Ye-Weddle.
g) Ukudidiyelwa koMthetho we-Romberg.

4. Uhlelo Lwezibalo Lwezibalo

a) Izindlela eziqondile
i. Umthetho kaCramer
ii. Omunye Umthetho We-Cramer
iii. Umthetho Wokuqedwa kwe-Gaussian
iv. I-Factorization ye-L&U Matrix
v. I-Factorization nge-Inverse Matrix
vi. Umthetho kaCholesky
vii. Umthetho we-Tri-Diagonal

b) Izindlela zokuphindaphinda
i. Indlela kaJacobi
ii. Indlela ye-Gauss-Seidel

Ubani ongasebenzisa lolu hlelo lokusebenza: Lolu hlelo lokusebenza luwusizo ngokulinganayo kubafundi kanye Kothisha ukuze baqonde isifundo futhi bakhombe amaphutha ezibalweni ezinde.

Lolu hlelo lokusebenza lunezici ezilandelayo ezibalulekile:
1. Kulula ukuyisebenzisa.
2. Bheka zonke izindlela ezijwayelekile.
3. Nikeza izixazululo ezinemininingwane (Isinyathelo ngesinyathelo).
4. Kulula ukuqonda izixazululo zezinkinga.