ikki o’lchovli issiqlik tarqalish tenglamasi to’r usulida yechish

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ikki o’lchovli issiqlik tarqalish tenglamasini to’r usulida yechish karimov umid ulug’bekovich urganch davlat universiteti ikki o’lchovli issiqlik tarqalish tenglamasi ikki o’lchovli issiqlik tarqalish tenglamasi quyidagi ko’rinishga ega ∂u ∂t = α ∂2u ∂x 2 + ∂2u ∂y 2  (1) bu yerda u(x , y , t) - koordinatalari (xi , yj) lardan iborat nuqtaning harorati α - issiqlik o’tkazuvchanlik koeffisienti t - vaqt karimov umid ulug’bekovich ikki o’lchovli issiqlik tarqalish tenglamasini to’r usulida yechish chekli ayirmalar ∂u ∂t ≈ un+1 − un ∆t (2) ∂2u ∂x 2 ≈ ui+1,j − 2ui ,j + ui−1,j ∆x 2 (3) ∂2u ∂y 2 ≈ ui ,j+1 − 2ui ,j + ui ,j−1 ∆y 2 (4) karimov umid ulug’bekovich ikki o’lchovli issiqlik tarqalish tenglamasini to’r usulida yechish chekli ayirmalar ∂u ∂t = α ∂2u ∂x 2 + ∂2u ∂y 2  (5) un+1 i ,j − un i ,j ∆t = α (un …

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) u(l, y , t) = g2(y) u(x , 0, t) = g3(x) u(x , l, t) = g4(x) karimov umid ulug’bekovich ikki o’lchovli issiqlik tarqalish tenglamasini to’r usulida yechish chegaraviy shartlar x o’q y o’q lx ly u(0, y , t) = g1(y) u(l, y , t) = g2(y) u(x , 0, t) = g3(x) u(x , l, t) = g4(x) karimov umid ulug’bekovich ikki o’lchovli issiqlik tarqalish tenglamasini to’r usulida yechish chegaraviy shartlar x o’q y o’q lx ly u(0, y , t) = g1(y) u(l, y , t) = g2(y) u(x , 0, t) = g3(x) u(x , l, t) = g4(x) karimov umid ulug’bekovich ikki o’lchovli issiqlik tarqalish tenglamasini to’r usulida yechish boshlang’ich va chegaraviy shartlar faraz qilaylik [0, lx ] tomon nx ta va [0, ly ] tomon esa mos holda ny ta kesmalarga ajratilgan bo’lsin. u holda ∆x = lx nx va ∆y = …

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ikki o’lchovli issiqlik tarqalish tenglamasini to’r usulida yechish karimov umid ulug’bekovich urganch davlat universiteti ikki o’lchovli issiqlik tarqalish tenglamasi ikki o’lchovli issiqlik tarqalish tenglamasi quyidagi ko’rinishga ega ∂u ∂t = α ∂2u ∂x 2 + ∂2u ∂y 2  (1) bu yerda u(x , y , t) - koordinatalari (xi , yj) lardan iborat nuqtaning harorati α - issiqlik o’tkazuvchanlik koeffisienti t - vaqt karimov umid ulug’bekovich ikki o’lchovli issiqlik tarqalish tenglamasini to’r usulida yechish chekli ayirmalar ∂u ∂t ≈ un+1 − un ∆t (2) ∂2u ∂x 2 ≈ ui+1,j − 2ui ,j + ui−1,j ∆x 2 (3) ∂2u ∂y 2 ≈ ui ,j+1 − 2ui ,j + ui ,j−1 ∆y 2 (4) karimov umid ulug’bekovich ikki o’lchovli issiqlik tarqalish …

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