Практикалық жұмыс №14
Тақырыбы: Кәдімгі дифференциалдық теңдеулерді жуықтап шешу әдістері Рунге –Кутта әдісі.
Мақсаты: Жылуөткізгіштік теңдеулері үшін айырымдық схемалармен танысу.
жылуөткізгіштік теңдеуі үшін аралас есеп бұл u(x,0) =f(x), 0≤х≤l бастапқы шартты және u(0,t) = , u(l ,t) = (t) шектік шарттарды, берілген теңдеуді қанағаттандыратын u(x,t) функцияны анықтау. Торлар әдісін қолданып, Ох осі бойынша h қадамын таңдайды, Оt осі бойынша қадамын есептейді , одан кейін xi=in, tj=jk (i-0,1,2,….,n; j=0,1,2,….,k) мәндерімен тор құрады.
uij=u(xij, tj) мәнін келесі формулалар арқылы есептейді:
ui0=u(xi,0)=f(xi) –бастапқы шарттан,
u0j=φ(tj), unj=ψ(tj)-шектік шарттардан.
Ішкі нүктелерде мәндерді анықтау үшін келесі формулалар қолданылады:
болғанда
болғанда
Тапсырма:
1. Торлар әдісін қолданып, параболалық типті дифференциалды теңдеу үшін аралас есептің шешімін құрыңыз.
2. Торлар әдісі арқылы программа жазып, оны ЭЕМ-да есептеп, нәтижелерін салыстырыңыз.
Орындау үлгісі:
Тапсырма. Торлар әдісін қолданып, (жылуөткізгіштік теңдеуі) параболалық типті дифференциалды теңдеу үшін аралас есептің шешімін құру. Бастапқы шарттар u(x,0)=3x(1-x)+0.12, u (0, t)=2(t+0.06), u(0.6;t)=0.84, мұндағы x Є . Есептеуді төрт ондық белгімен t![](data:image/png;base64,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) үшін h=0,1 болғанда орындау, деп санаймыз.
Шығарылымы:
Параболалық теңдеу, торлар әдісімен u(xi,ti) функция мәндерінен u(xi,tj+1) мәндеріне біртіңдеп өтумен есептеледі. Мұндағы tj+1= tj+k, где k=h/6=0,01/6=0,017.
Есептеуді келесі формуламен жүргіземіз:
ui,j+1= ( ui+1,j +4ui,j+ ui-1,j) (i=1,2,3,4,5,6; j=1,2,3,4,5,6).
Барлық есептеулер кестеде келтірілген:
j
|
i
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
|
|
0
|
0,1
|
0,2
|
0,3
|
0,4
|
0,5
|
0,6
|
0
|
0
|
0,12
|
0,39
|
0,60
|
0,75
|
0,84
|
0,87
|
0,84
|
1
|
0,0017
|
0,1233
|
0,3800
|
0,5900
|
0,7400
|
0,8300
|
0,8600
|
0,84
|
2
|
0,0033
|
0,1267
|
0,6372
|
0,5800
|
0,7300
|
0,8200
|
0,8517
|
0,84
|
3
|
0,0050
|
0,1300
|
0,3659
|
0,5704
|
0,7200
|
0,8103
|
0,8445
|
0,84
|
4
|
0,0067
|
0,1333
|
0,3607
|
0,5612
|
0,7101
|
0,8010
|
0,8380
|
0,84
|
5
|
0,0083
|
0,1367
|
0,3562
|
0,5526
|
0,7004
|
0,7920
|
0,8322
|
0,84
|
6
|
0,01
|
0,1400
|
0,3524
|
0,5445
|
0,6910
|
0,7834
|
0,8268
|
0,84
|
Есеп беру:
1. Лабораториялық жұмыстың аты.
2. Жеке тапсырма.
3. Теориялық бөлімі.
4. Программа мәтіні.
5. Есептеу нәтижесі.
Өздік жұмысы:
Тапсырма: Торлар әдісін қолданып, (жылуөткізгіштік теңдеуі) параболалық типті дифференциалды теңдеу үшін аралас есептің шешімін құру. Бастапқы шарттар u(x,0) = f(x), u(0,t) = , u(0,6,t) = (t), мұндағы x Є . Есептеуді төрт ондық белгімен t![](data:image/png;base64,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) үшін h=0,1 болғанда орындау, деп санаймыз.
№1. u(x,0)=cos2x, u(0,t)=1-6t, u(0,6;t)=0,3624.
№2. u(x,0)=x(x+1), u(0,t)=0, u(0,6;t)=2t+0,96.
№3. u(x,0)=1,2+lg(x+0,4), u(0;t)=0,8+t, u (0,6;t).
№4. u(x,0)=sin2x, u(0,t)= 2t, u(0,6;t)=0,932.
№5. u(x,0)=3x(2-x), u(0,t)=0, u(0,t)=(0,6;t)=2t+2,52.
№6. u(x,0)=1-lg(x+0,4), u(0,t)=1,4, u(0,6;t)=t+1.
№7. u(x,0)=sin(0,55x+0,03), u(0;t)=t+0,03, u(0,6;t)=0,354.
№8. u(x,0)=2x(1-x)+0,2, u(0,t)=0,2, u(0,6;t)=t+0,68.
№9. u(x,0)=sinx+0,08, u(0,t)=0,08+2t, u(0,6;t)=0,6446.
№10. u(x,0)=cos(2x=0,19), u(0,t)=0,932, u(0,6;t)=1798.
№11. u(x,0)=2x(x=0,2)+0,4, u(0,t)=2t+0,4, u(0,6;t)=1,36.
№12. u(x,0)=lg(x+0,26)+1, u(0;t)=0,415+t, u(0,6;t)=0,9345.
№13. u(x,0)=sin(x+0,45), u(0,t)=0,435-2t, u(0,6t)=0,8674.
№14. u(x,0)=0,3+x(x+0,4), u(0,t)=0,3, u(0,6;t)=6t+0,9.
№15. u(x,0)=(x-0,2)(x+1)+2; u(0,t)=6t; u(0,6;t)=0,84
№16. u(x,0)=x(0,3+2x), u(0,t)=0, u(0,6;t)=6t+9.
№17. u(x,0)=sin(x+0,48), u(0,t)=0,4618, u(0,6;t)=3t+0,882.
№18. u(x,0)=sin(x+0,02), u(0,t)=3t+0,02, u(0,6;t)=0,581.
№19. u(x,0)=cos(x+0,48),u(0,t)=6t+0,887, u(0,6t)=0,4713.
№20. u(x,0)=lg(2,63-x) u(0,t)=3(0,14-t), u(0,6;t)=0,3075.
№21. u(x, 0) =1.5-x(1-x), u (0, t)=3(0.5-t), u(0.6;t)=1.26.
№22. u(x, 0) =cos(x+0.845), u (0, t)=6(t+0.11), u(0.6;t)=0.1205.
№23. u(x, 0) =lg(2.24+x), u (0, t)=0.3838, u(0.6;t)=6(0.08-t).
№24. u(x, 0) =0.6+x(0.8-x), u (0, t)=0.6, u(0.6;t)=3(0.24+t).
№25. u(x, 0) =cos(x+0.66), u (0, t)=3t+0.79, u(0.6;t)=0.3058.
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