Numeric Methods/Workspace
v2
DSH-000MAIN · DASHBOARD / MK-1
Sonli usullar / Laboratoriya

Matematikani hisoblab
, har qadamni tushuning.

Sonli usullarni nazariya bilan emas, real interaktiv hisoblash orqali o'rganing.

01 / OVERVIEW

Workspace holati

SYS
01AFaol usullar09 ta metod↗
02BHisoblash sohalari5 ta toifa↗
03CHisoblash muhiti100% Client-side↗
02 / METODLAR KATALOGI

Interaktiv sonli usullar laboratoriyasi

HUB
01 / ALGTenglamalar

Teng ikkiga bo'lish

Oraliqni teng ikkiga bo'lib, uzluksiz tenglama ildizini kafolatli yaqinlashtirish.

c=a+b2,f(a)⋅f(c)<0c = \frac{a+b}{2}, \quad f(a) \cdot f(c) < 0
Yaqinlashish:O(log⁡2(1/ε))O(\log_2(1/\varepsilon))Laboratoriyaga
02 / ALGTenglamalar

Nyuton usuli

Hosila asosida urinma qurib, ildizga tez yaqinlashish va har bir qadamni tekshirish.

xn+1=xn−f(xn)f′(xn)x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}
Yaqinlashish:O(log⁡log⁡(1/ε))O(\log\log(1/\varepsilon))Laboratoriyaga
03 / LINChiziqli sistemalar

Haydash usuli

Uch diagonalli chiziqli tenglamalar sistemasini to‘g‘ri va teskari yurish bilan yechish.

aixi−1+bixi+cixi+1=dia_i x_{i-1} + b_i x_i + c_i x_{i+1} = d_i
Yaqinlashish:O(n)O(n)Laboratoriyaga
04 / INTInterpolyatsiya

Lagranj interpolyatsiyasi

Diskret nuqtalar to'plamidan o'tuvchi yagona interpolyatsion ko'phadni qurish.

Ln(x)=∑i=0nyi∏j≠ix−xjxi−xjL_n(x) = \sum_{i=0}^n y_i \prod_{j \neq i} \frac{x - x_j}{x_i - x_j}
Yaqinlashish:O(n2)O(n^2)Laboratoriyaga
05 / QUAIntegrallash

To‘g‘ri to‘rtburchaklar

Chap, o'ng va o'rta nuqtalar yordamida aniq integralni sonli yaqinlashtirish.

I≈h∑i=0n−1f(xi∗),xi∗∈{xi,xi+1}I \approx h \sum_{i=0}^{n-1} f(x_i^*), \quad x_i^* \in \{x_i, x_{i+1}\}
Yaqinlashish:O(h)…O(h2)O(h) \dots O(h^2)Laboratoriyaga
06 / QUAIntegrallash

Trapetsiya usuli

Egri chiziqli trapetsiyani to'g'ri chiziqli bo'laklar bilan approksimatsiya qilish.

I≈h2[y0+2∑i=1n−1yi+yn]I \approx \frac{h}{2} \left[ y_0 + 2\sum_{i=1}^{n-1} y_i + y_n \right]
Yaqinlashish:O(h2)O(h^2)Laboratoriyaga
07 / QUAIntegrallash

Simpson usuli

Parabolalar yordamida aniq integralni 4-tartibli yuqori aniqlikda hisoblash.

I≈h3[y0+4∑toqyi+2∑juftyi+yn]I \approx \frac{h}{3} \left[ y_0 + 4\sum_{\text{toq}} y_i + 2\sum_{\text{juft}} y_i + y_n \right]
Yaqinlashish:O(h4)O(h^4)Laboratoriyaga
08 / ODEDifferensial

Eyler usullari

Koshi masalasini birinchi tartibli differensial tenglama orqali qadamma-qadam yechish.

yi+1=yi+h⋅f(xi,yi),y(x0)=y0y_{i+1} = y_i + h \cdot f(x_i, y_i), \quad y(x_0) = y_0
Yaqinlashish:O(h)O(h)Laboratoriyaga
09 / ODEDifferensial

Runge–Kutta 4-tartibli usuli

Birinchi tartibli Koshi masalasini klassik to‘rtinchi tartibli Runge–Kutta usuli bilan yeching.

yi+1=yi+k0+2k1+2k2+k36y_{i+1}=y_i+\frac{k_0+2k_1+2k_2+k_3}{6}
Yaqinlashish:O(h4)O(h^4)Laboratoriyaga
Keyingi qadam

Birinchi usulni sinab ko'ring

Funksiya, oraliq va aniqlikni kiriting. Tizim ildizga yaqinlashishning har bir qadamini ko'rsatadi.

Laboratoriyani boshlash