Kurs ishlari mavzulari banki va ularni bajarishga oid uslubiy tavsiyalar

V. Oddiy differensial tenglamalarni sonli yechish.

1. 
   Oddiy differensial tenglamalarni taqribiy yechishning klassik, modifikatsiyalangan, rivojlantirilgan Eyler usullari.
   

Namunaviy misol: Ushbu y = y³, y(0) = 0.5 Koshi masalasining [0, 2] kesmadagi sonli yechimini h = 0.2 qadam bilan toping.

2. 
   Oddiy differensial tenglamalarni taqribiy yechishning klassik Eyler va Eyler-Koshi usullari.
   

Namunaviy misol: Ushbu y = - y² + 2/x², y(1) = 0 Koshi masalasining [1, 3] kesmadagi sonli yechimini h = 0.2 qadam bilan toping.

3. 
   Oddiy differensial tenglamalarni taqribiy yechishning Eyler va Runge-Kutta usullari.
   

Namunaviy misol: Ushbu y = x², y(0) = 1 Koshi masalasining [0, 2] kesmadagi sonli yechimini h = 0.2 qadam bilan toping.

4. 
   Oddiy differensial tenglamalarni taqribiy yechishning Runge-Kutta-Gill va Kutta-Merson usullari.
   

Namunaviy misol: Ushbu y + y + y³ = cos(x), y(0) = 2 Koshi masalasining [0, 2] kesmadagi sonli yechimini h = 0.2 qadam bilan toping.

5. 
   Oddiy differensial tenglamalarni taqribiy yechishning Adams va Adams-Krilov usullari.
   

Namunaviy misol: Ushbu y + y = cos(xy), y(0) = 1 Koshi masalasining [0, 2] kesmadagi sonli yechimini h = 0.2 qadam bilan toping.

6. 
   Oddiy differensial tenglamalarni taqribiy yechishning Adams va Miln usullari.
   

Namunaviy misol: Ushbu y + y = sin(xy), y(0) = 2 Koshi masalasining [0, 2] kesmadagi sonli yechimini h = 0.2 qadam bilan toping.

7. 
   Oddiy differensial tenglamalarni taqribiy yechishning Xemming va Adams-Beyshfort usullari.
   

Namunaviy misol: Ushbu y + y + y³ = cos(5x), y(0) = 3 Koshi masalasining [0, 2] kesmadagi sonli yechimini h = 0.2 qadam bilan toping.

8. 
   Oddiy differensial tenglamalarni taqribiy yechishning Adams-Multon va Miln usullari.
   
9. 
   Oddiy differensial tenglamalarni bir qadamli usullar (Eyler, Runge-Kutta, Kutta-Merson usullari) bilan taqribiy yechish.
   
10. 
    Oddiy differensial tenglamalarni prediktor-korrektor tipidagi usullar (Adams-Beyshfort, Adams-Multon va Miln usullari) yordamida taqribiy yechish.
    
11. 
    Oddiy differensial tenglamalarni ko‘p qadamli usullar (Adams va Miln usullari) yordamida taqribiy yechish.
    
12. 
    Qat’iy differensial tenglamalarni taqribiy yechish usullari.
    
13. 
    Qat’iy bo‘lmagan differensial tenglamalarni taqribiy yechish usullari.
    
14. 
    Birinchi tartibli oddiy differensial tenglamalar sistemasini yechishning sonli usullari.