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Задания к лабораторным работам



 

Таблица 14. Варианты заданий к лабораторной работе №1

 

Задача переноса
ut +(1 – x2 + t2) ux = cos(p x/2), u(x,0) =1 – x2, 0£ x £1, u(0,t) = t/2 + 1,0£ t £1
ut +(cos(p x/2) + t) ux = x sin(p x/2), u(x,0) =1 – x2, 0£ x £1, u(0,t) =cos(p t/2),0£ t £1
ut +(cos(p x/2) + t) ux = t arctg(x), u(x,0) =1 – x2, 0£ x £1, u(0,t) =(t +2)/2,0£ t £1
ut +arctg(x/(1 + t)) ux = t/(1 + x), u(x,0) =cos(p x/2), 0£ x £1, u(0,t) = t + 1,0£ t £1
ut +(1 + t + x2) ux = lg(10 + t), u(x,0) =2 x, 0£ x £1, u(0,t) =2 sin(p t/2),0£ t £1
ut +(sin(p x/2) + t2) ux = 10,3 t, u(x,0) =1 - x, 0£ x £1, u(0,t) =cos(p t/2),0£ t £1
ut +(sin(p t/2) + x2) ux = 1,2 t – t2, u(x,0) =2 x – x2, 0£ x £1, u(0,t) =2 sin(pt/2),0£ t £1
ut +(1,20,2 t + sin(p t/2)) ux = t + x, u(x,0)= x – x2, 0£ x £1, u(0,t) =sin(p t/2),0£ t £1
ut +(10,5 t + sin(p t/2)) ux = x/(1+t), u(x,0) =cos(p x/2), u(0,t) = t + 1, 0£ x £1,0£ t £1
ut +(1 + t + x2) ux = sin2(p t/2), u(x,0) =1 + x, 0£ x £1, u(0,t) =1 – t,0£ t £1
ut +(1 + sin(p x/2)) ux = x/(1+t2), u(x,0) =cos(p x/2), 0£ x £1, u(0,t) = t + 1,0£ t £1
ut +(1 + x2)(1 + t) ux = ln(2 + t), u(x,0) =cos(p x/2), 0£ x £1, u(0,t) = t +1,0£ t £1
ut +(0,25 + t + x2) ux = x2 + t2, u(x,0) =(x + 0,5)cos(x/2), u(0,t) =(t + 1)/2, 0£ x £1,0£ t £1

 


Таблица 14. Варианты заданий к лабораторной работе №1

 

Задача переноса
ut +(1 + x2) ux = sin2(x + t), u(x,0) = 2x, 0£ x £1, u(0,t) = 2t,0£ t £1
ut +(2 - t + x2) ux =lg(2 + t), u(x,0) =1 +x2, 0£ x £1, u(0,t) = 1 + t,0£ t £1
ut +(0,25 + t + x2) ux = t2 + x2, u(x,0) =(1 + x)x, 0£ x £1, u(0,t) =2 t,0£ t £1
ut +(0,25 + x + t2) ux = x2 - t2, u(x,0) = x - x2, 0£ x £1, u(0,t) = t,0£ t £1
ut +(1 + t2)(1 + x) ux = arctg(x/(1 + t)), u(x,0) = x/2 + 1, u(0,t) = t + 1, 0£ x £1,0£ t £1
ut +(1 + t2 + x2) ux = sin2(p x/2), u(x,0) = x + 0,5, 0£ x £1, u(0,t) =2t + 0,5,0£ t £1
ut +(1,2 + x - t2) ux = t sin(p x/2), u(x,0) =cos(x), 0£ x £1, u(0,t) = t +1,0£ t £1
ut +(cos(p x/2) + t) ux = t – x, u(x,0) =1 – x, 0£ x £1, u(0,t) = 1 + t,0£ t £1
ut +(sin(pt/2) + 1) ux = 2(1 - x), u(x,0) = x + 2, 0£ x £1, u(0,t) =2 - t,0£ t £1
ut +arctg(t/(1 + x)) ux = x + 2 t, u(x,0) = x, 0£ x £1, u(0,t) =sin(t),0£ t £1
ut +(sin(p t/2) + x) ux = e t - x, u(x,0) = x2/2, 0£ x £1, u(0,t) = 2 t,0£ t £1
ut +(sin(p x/2) + t2) ux = 2 x + t, u(x,0) =1 - x2/2, 0£ x £1, u(0,t) = t + 1,0£ t £1
ut +(1 + t)(1 + x2) ux = 1 – t + x, u(x,0) = x + 1, 0£ x £1, u(0,t) =cos(p t/2),0£ t £1
ut +(1,20,2 t +x) ux = t + x, u(x,0) = x/2, 0£ x £1, u(0,t) = t/2,0£ t £1
ut +(1 + t - x2) ux = arctg(x + t), u(x,0) = x/2, 0£ x £1, u(0,t) = 2 t,0£ t £1

Таблица 14. Варианты заданий к лабораторной работе №1



 

Задача переноса
ut +(1 + t + x2) ux = sin(p x), u(x,0) = x(1 - x), 0£ x £1, u(0,t) =sin(t),0£ t £1
ut +(1 + sin(p x/2)) ux = x - t, u(x,0) = x/2, 0£ x £1, u(0,t) = t,0£ t £1
ut +(1 + x2)(1 - t) ux = t + x, u(x,0) = x – 0,5, 0£ x £1, u(0,t) = t – 0,5,0£ t £1
ut +(0,25 + t + x2) ux = x/(1+t2), u(x,0) = x + 0,5, 0£ x £1, u(0,t) = t + 0,5,0£ t £1
ut +(1 - t + x2) ux = x – 2 t, u(x,0) =1/(1 + x), 0£ x £1, u(0,t) = cos(t),0£ t £1
ut +(2 - t + x2) ux = x cos(p x), u(x,0) = x2/2, 0£ x £1, u(0,t) = 2 t,0£ t £1
ut +(0,25 + t)(1 + x2) ux = t x, u(x,0) =cos(p x/2), 0£ x £1, u(0,t) = 1,0£ t £1
ut +(t2 + x2) ux = t x, u(x,0) =1 - x, 0£ x £1, u(0,t) =1 + t,0£ t £1
ut +(1 + t2)(1 + x) ux = sin(x + t), u(x,0) = cos(x), 0£ x £1, u(0,t) = 1 - t,0£ t £1
ut +(1 + t2 + x2) ux = cos(t x), u(x,0) = x(1 - x), 0£ x £1, u(0,t) = t,0£ t £1
ut +(1,2 + x - t2) ux = x + t, u(x,0) =0,5 + x, 0£ x £1, u(0,t) =2 t + 0,5,0£ t £1
ut +(1,5 + t – 0,5x) ux = x2 + t2, u(x,0) =sin(x), 0£ x £1, u(0,t) = t,0£ t £1

 

Таблица 15. Варианты заданий к лабораторной работе №2

 

Задача теплопереноса
ut - (1 + t x) uxx = 2 x, u(x,0) = cos(px), 0£ x £1, - ux(0,t) = - t, ux(1,t) + s1 u(1,t) = t - 1,0£ t £1, s1 = - 0,7; 1
ut - (1 + t2 + x) uxx = xsin(px), u(x,0) = x2, 0£ x £1, - ux(0,t) + s0 u(0,t) = t, u(1,t) = cos(pt/2),0£ t £1, s0 = - 2; 1
ut - (1 + t – x2) uxx = x2 – t2, u(x,0) = 0,5x2, 0£ x £1, - ux(0,t) + s0×u(0,t) = 2t, ux(1,t) = 1 - t,0£ t £1, s0 = - 2,5; 3
ut - (1 + t - x) uxx = x - t2, u(x,0) = x +1, 0£ x £1, - ux(0,t) = t +1, ux(1,t) + s1 u(1,t) = (t + 2)/2,0£ t £1, s1 = - 1; 1,5
ut - arctg((1 + x)/(1 + t2)) uxx = 1+ 0,2t, u(x,0) = 1 - x, 0 £ x £ 1, u(0,t) = t +1, ux(1,t) + s1 u(1,t) = t - 1,0£ t £1, s1 = - 2; 1
ut - (1 - 0,5t + x2) uxx = 2sin(pt/2), u(x,0) = 1 - x, 0£ x £1, u(0,t) = 1, ux(1,t) + s1 u(1,t) = 2t - 1,0£ t £1, s1 = - 2; 1
ut - (1 + t)(1 + x2) uxx = 1 +2tx, u(x,0) = x, 0£ x £1, u(0,t) = 2t, ux(1,t) + s1 u(1,t) = t + 2,0£ t £1, s1 = - 3; 3
ut - (1 + t)(1 + x) uxx = cos(tx), u(x,0) =1 - x, 0£ x £1, u(0,t) = cos(t), ux(1,t) + s1 u(1,t) = 2t - 1,0£ t £1, s1 = - 2; 3
ut - (t + cos(px/2)) uxx = 1 + tx, u(x,0) = x2/2, 0£ x £1, - ux(0,t) + s0×u(0,t) = 0,2 t, ux(1,t) = 0,0£ t £1, s0×= - 0,5; 2
ut - (1 + sin(px/2)) uxx = 1 + t, u(x,0) = x2/2, 0£ x £1, - ux(0,t) + s0×u(0,t) = 0, ux(1,t) = 2t + 1,0£ t £1, s0 = - 1; 2

 


 

Таблица 15. Варианты заданий к лабораторной работе №2

 

Задача теплопереноса
ut - (1+ x/(1+t2)) uxx = 1 - t, u(x,0) = cos(px), 0£ x £1, - ux(0,t) + s0×u(0,t) = 2t - 1, ux(1,t) + u(1,t) = -1,0£ t £1, s0×= - 1; 2
ut - arctg(x/(1+t2)) uxx = tx, u(x,0) = 1 - x, 0£ x £1, u(0,t) = 1 + t, ux(1,t) + s1 u(1,t) = t2- 1,0£ t £1, s1 = - 2; 1
ut - cos(x/(1+t)) uxx = x + t, u(x,0) = sin(px), 0£ x £1, u(0,t) = 2t, ux(1,t) + s1 u(1,t) = arctg(t - 1),0£ t £1, s1 = - 1,3; 1
ut - (t + arctg(x/(1+t2))) uxx = x + t, u(x,0) = cos(px), 0£ x £1, u(0,t) = t +1, ux(1,t) + s1 u(1,t) = t - 1,0£ t £1, s1 = - 1,5; 2,3
ut - (1 + sin2(x + t)) uxx = 1 + t, u(x,0) = xsin(px), 0£ x £1, - ux(0,t) + s0×u(0,t) = 2t, u(1,t) = - t,0£ t £1, s0 = - 2; 3
ut - (1 + cos2(x + t)) uxx = e t- x, u(x,0) = ln(1 + x), 0£ x £1, - ux(0,t) + s0×u(0,t) = 1 + t, ux(1,t) = (1 - t)/2,0£ t £1, s0 = - 2; 1,7
ut - (t + sin2x) uxx = t - cos2x, u(x,0) = x2/2, 0£ x £1, ux(0,t) = 0, ux(1,t) + s1 u(1,t) = t +2,0£ t £1, s1 = - 2; 3
ut - ((1 + x)/(1 + t)) uxx = tx, u(x,0) = xsin(px), 0£ x £1, - ux(0,t) + s0×u(0,t) = sin(t), u(1,t) = -2t,0£ t £1, s0 = - 0,5; 2
ut - (t + sin2(px/2)) uxx = tx, u(x,0) = cos2(px/2), 0£ x £1, - ux(0,t) + s0×u(0,t) = cos(t), u(1,t) = - t,0£ t £1, s0 = -2; 0,5
ut - (x2 + t2) uxx = x + 2t, u(x,0) = 1 - x2, 0£ x £1, ux(0,t) = 0, ux(1,t) + s1 u(1,t) = 2t,0£ t £1, s1 = - 2; 1

 


 

Таблица 15. Варианты заданий к лабораторной работе №2

 

Задача теплопереноса
ut - (1 – x2 + t2) uxx = cos(px/2), u(x,0) = 1 – x2, 0£ x £1, - ux(0,t) = - t, ux(1,t) + s1 u(1,t) = t - 2,0£ t £1, s1 = - 1,7; 2,5
ut - (cos(px/2) + t) uxx = x sin(px/2), u(x,0) = 1 - x2, 0£ x £1, - ux(0,t) + s0×u(0,t) =cos(pt/2), u(1,t) = t/2,0£ t £1, s0 = - 2; 1
ut - (cos(p x/2) + t) uxx = t arctg(x), u(x,0) = 1 - x2, 0£ x £1, - ux(0,t) + s0×u(0,t) =(t - 1)/2, ux(1,t) = -2 + t,0£ t £1, s0 = - 0,5; 1
ut - arctg(x/(1 + t)) uxx = t/(1 + x), u(x,0) = cos(p x/2), 0£ x £1, - ux(0,t) + s0×u(0,t) = t +1, ux(1,t) = (t - 3)/2,0£ t £1, s0 = - 0,5; 3
ut - (1 + t + x2) uxx = lg(10 + t), u(x,0) = 2 x, 0£ x £1, - ux(0,t) + s0×u(0,t) =2cos(p t/2), u(1,t) = t + 2,0£ t £1, s0 = - 2; 1
ut - (sin(p x/2) + t2) uxx = 10,3 t, u(x,0) = 1 - x, 0£ x £1, - ux(0,t) + s0 u(0,t)=2cos(p t/2), ux(1,t) + u(1,t)=2 t - 1, 0 £ t £ 1, s0 = - 1; 3,5
ut - (sin(p t/2) + x2) uxx = 1,2 t – t2, u(x,0) = 2 x – x2, 0£ x £1, - ux(0,t) + s0×u(0,t) =2 cos(pt/2), u(1,t) = t + 1,0£ t £1, s0 = - 2; 3
ut - (1,2 + 0,2 t + sin(p t/2)) uxx = t + x, u(x,0) = x – x2, 0£ x £1, - ux(0,t) + s0 u(0,t) =1 + sin(p t/2), ux(1,t) = 2 t - 1,0£ t £1, s0 = - 1; 3
ut - (1 + 0,5 t + sin(p t/2)) uxx = x/(1+t), u(x,0) = cos(p x/2), - ux(0,t) + s0 u(0,t) = t + 1, u(1,t) = 0,0£ t £1,, 0£ x £1 s0 = - 2; 1
ut - (1 + t + x2) uxx = sin2(p t/2), u(x,0) = 2 x, 0£ x £1, - ux(0,t) + s0 u(0,t) =2 – t, ux(1,t) =2 + t,0£ t £1, s0 = - 2; 2

 

Таблица 15. Варианты заданий к лабораторной работе №2

 

Задача теплопереноса
ut - (1 + sin(p x/2)) uxx = x/(1+t2), u(x,0) = cos(p x/2), 0£ x £1, - ux(0,t) + s0×u(0,t) = t + 1, u(1,t) = 0,0£ t £1, s0 = - 1; 1,5
ut - (1 + x2)(1 + t) uxx = lg(1 + t), u(x,0) = cos(p x/2), 0£ x £1, - ux(0,t) + s0 u(0,t) =(t - 1)/2, u(1,t) = t2,0£ t £1, s0 = - 0,5; 3
ut - (0,25 + t + x2) uxx = x2 + t2, u(x,0) = cos(p x/2), 0£ x £1, - ux(0,t) + s0 u(0,t) =(t - 1)/2, u(1,t) = 0,0£ t £1, s0 = - 0,5; 1
ut - (1 + x2) uxx = sin2(x + t), u(x,0) = 2 x, 0£ x £1, - ux(0,t) + s0×u(0,t) = 2 - t, u(1,t) = t + 2,0£ t £1, s0 = - 2; 2
ut - (2 + t + x2) uxx = lg(2 + t), u(x,0) = 1 +x2, 0£ x £1, - ux(0,t) + s0×u(0,t) = 1 + t, u(1,t) = 2 - t,0£ t £1, s0 = - 0,7; 3
ut - (0,25 + t + x2) uxx = t2 + x2, u(x,0) = (1 + x)x, 0£ x £1, - ux(0,t) + s0×u(0,t) =2 t - 1, u(1,t) = 2 - t,0£ t £1, s0 = - 1; 2
ut - (0,25 + x + t2) uxx = x2 - t2, u(x,0) = x - x2, 0£ x £1, - ux(0,t) + s0×u(0,t) = t + 1, ux(1,t) = t - 1,0£ t £1, s0 = - 1; 2
ut - (1 + t2)(1 + x) uxx = arctg(x/(1 + t)), u(x,0) = x/2, 0£ x £1, - ux(0,t) + s0×u(0,t) = t - 1, u(1,t) = 1 - t,0£ t £1, s0 = - 2; 1
ut - (1 + t2 + x2) uxx = sin2(p x/2), u(x,0) = x + 0,5, 0£ x £1, - ux(0,t) + s0×u(0,t) =2 t, u(1,t) = 0,5 - t,0£ t £1, s0 = - 2; 5
ut - (1,2 + x - t2) uxx = t sin(p x/2), u(x,0) = cos(p x/2), 0£ x £1, - ux(0,t) + s0×u(0,t) = t - 1, ux(1,t) = t,0£ t £1, s0 = - 1; 1

Таблица 16. Варианты заданий к лабораторной работе №3

Волновая задача
utt - (cos(p x/2) + t) uxx = t - x, u(x,0) = 1 - x, ut(x,0) = 0,5x, 0£ x £1, - ux(0,t) + s0×u(0,t) = 1 + t, ux(1,t) = - cos(p t/2), 0£ t £1, s0 = - 1; 2,5,
utt - (sin(p t/2) + 1) uxx = 2(1 - x), u(x,0) = x – 0,5, ut(x,0) = 0,5x2, 0£ x £1, - ux(0,t) = 1 + t, ux(1,t) + s1 u(1,t) = 2 - t, 0£ t £1, s1 = - 1,7; 2
utt - arctg((1 + t)/(1 + x)) uxx = x + 2 t, u(x,0) = x, ut(x,0) = 0, 0£ x £1, u(0,t) = 2 t, ux(1,t) + s1 u(1,t) = 2 cos(t),0£ t £1, s1 = - 3; 2
utt - (sin(p t/2) + x) uxx = e t - x, u(x,0) = x2/2, ut(x,0) = x, 0£ x £1, - ux(0,t) + s0 u(0,t) = 2t, ux(1,t) +2 u(1,t) = 2 - t, 0£ t £1, s0 = - 2; 3,5
utt - (sin(p x/2) + t2) uxx = 2 x + t, u(x,0) = 1 - x2/2, ut(x,0) = 0,5x, 0£ x £1, - ux(0,t) + s0×u(0,t) = t +1, ux(1,t) + 2 u(1,t) = 0, 0£ t £1, s0 = - 1; 1,5
utt - (1 + t)(1 + x2) uxx = 1 – t + x, u(x,0) = x/2, ut(x,0) = (1 - x)/2, 0£ x £1, u(0,t) = 2 t, ux(1,t) + s1 u(1,t) = 1, 0£ t £1, s1 = - 1,3; 1
utt - (1,2 + 0,2 t +x) uxx = t + x, u(x,0) = x/2, ut(x,0) = 0,3x, 0£ x £1, - ux(0,t) + s0 u(0,t) = t/2, ux(1,t) + b u(1,t) = 1 +t2, 0£ t £1, s0 = - 0,5; 2
utt - (1 + t - x2) uxx = arctg(x + t), u(x,0) = x/2, ut(x,0) = x – 0,5, 0£ x £1, - ux(0,t) + s0×u(0,t) = 2t - 1, u(1,t) = t/2, 0£ t £1, s0 = - 2; 3

Таблица 16. Варианты заданий к лабораторной работе №3

Волновая задача
utt - (1 + t + x2) uxx = sin(p x), u(x,0) = x(1 - x), ut(x,0) = 0,3 x, 0£ x £1, u(0,t) = - t, ux(1,t) + s1 u(1,t) = t - 1, 0£ t £1, s1 = - 2; 2
utt - (1 + sin(p x/2)) uxx = x - t, u(x,0) = x/2, ut(x,0) = 0,5, 0£ x £1, u(0,t) = 0, ux(1,t) + s1 u(1,t) = t2 + 1, 0£ t £1, s1 = - 1; 2
utt - (1 + x2)(1 + t) uxx = t + x, u(x,0) = x – 0,5, ut(x,0) = x/3, 0£ x £1, u(0,t) = (t - 1)/2, ux(1,t) + s1u(1,t) = t + 2, 0£ t £1, s1 = - 1; 2
utt - (0,25 + t + x2) uxx = x/(1+t2), u(x,0) = x – 0,5, ut(x,0) =sin(p x), 0£ x £1, - ux(0,t) = t – 0,5, ux(1,t) + s1 u(1,t) = t + 2, 0£ t £1, s1 = - 3; 2
utt - (1 + t + x2) uxx = x – 2 t, u(x,0) = 1/(1 + x), ut(x,0) = 0,3x, 0£ x £1, - ux(0,t) + s0 u(0,t) = t - 2,2ux(1,t) + u(1,t) = 0, 0£ t £1, s0 = - 1; 2
utt - (2 + t – x2) uxx = x cos(p x), u(x,0) = x2/2, ut(x,0) = 0,5x, 0£ x £1, - ux(0,t) = t, ux(1,t) + s1 u(1,t) = 2 - t, 0£ t £1, s1 = - 0,5; 2
utt - (0,25 + t)(1 + x2) uxx = t x, u(x,0) = sin(p x/2), ut(x,0) = x, 0£ x £1, - ux(0,t) = (1 - t)/2, ux(1,t) + s1 u(1,t) = 1 + 2t, 0£ t £1, s1 = - 2; 3
utt - (t2 + x2) uxx = t x, u(x,0) = 1 - x, ut(x,0) = x/2, 0£ x £1, u(0,t) = 0,2 e t, ux(1,t) + s1 u(1,t) = t - 1, 0£ t £1, s1 = - 2; 1

Таблица 16. Варианты заданий к лабораторной работе №3

Волновая задача
utt - (1 + t2)(1 + x) uxx = sin(x + t), u(x,0) = cos(x), ut(x,0) = sin(x), 0£ x £1, - ux(0,t) + s0×u(0,t) = 2 - t, u(1,t) = cos(1 - t), 0£ t £1, s0 = - 0,5; 2
utt - (1 + t2 + x2) uxx = cos(t x), u(x,0) = x(1 - x), ut(x,0) = 0,5x, 0£ x £1, - ux(0,t) = 0, ux(1,t) + s1 u(1,t) = t + 1, 0£ t £1, s1 = - 1; 2
utt - (1,2 + x + t2) uxx = x + t, u(x,0) = 0,5 + x, ut(x,0) = x/2, 0£ x £1, - ux(0,t) = (1 - t)/2, ux(1,t) + s1 u(1,t) = 2 t +1, 0£ t £1, s1 = - 0,5; 2,5
utt - (1,5 + t – 0,5x) uxx = x2 + t2, u(x,0) = cos(x), ut(x,0) = sin(x), 0£ x £1, u(0,t) = 1 + t, ux(1,t) + s1 u(1,t) = t + 0,5, 0£ t £1, s1 = - 1; 1,5
utt - (1 + t x) uxx = 2x, u(x,0) = cos(p x), ut(x,0) = 0,5x, 0£ x £1, - ux(0,t) = - t, ux(1,t) + s1 u(1,t) = t - 1,0£ t £1, s1 = - 0,7; 1
utt - (1 + t2 + x) uxx = x sin(px), u(x,0) = x2, ut(x,0) = x2, 0£ x £1, - ux(0,t) + s0 u(0,t) = t, u(1,t) = cos(p t/2), 0£ t £1, s0 = - 2; 1
utt - (1 + t – x2) uxx = x2 – t2, u(x,0) = 0,5x2, ut(x,0) = 0, 0£ x £1, - ux(0,t) + s0×u(0,t) = 2t, ux(1,t) = (1 – t)/2, 0£ t £1, s0 = - 1,5; 3
utt - (1 + t - x) uxx = x - t2, u(x,0) = x +1, ut(x,0) = x, 0£ x £1, - ux(0,t) = t +1, ux(1,t) + s1 u(1,t) = t + 2, 0£ t £1, s1 = - 1; 2,5

Таблица 16. Варианты заданий к лабораторной работе №3

Волновая задача
utt - arctg((0,5 + x)/(1 + t2)) uxx = 1+ 0,2 t, u(x,0) = 1 - x, ut(x,0) = 0,5x, 0£ x £1, u(0,t) = t +1, ux(1,t) + s1 u(1,t) = t - 1, 0£ t £1, s1 = - 2; 1
utt - (1 + 0,5t + x2) uxx = 2 sin(p t/2), u(x,0) = 1 - x, ut(x,0) = (1 - x)/2, 0£ x £1, u(0,t) = 1, ux(1,t) + s1 u(1,t) = 2 t - 1, 0£ t £1, s1 = - 2; 1
utt - (1 + t)(1 + x2) uxx = 1 +2 t x, u(x,0) = x, ut(x,0) = 0,3x, 0£ x £1, u(0,t) = 2 t, ux(1,t) + s1 u(1,t) = t + 2,0£ t £1, s1 = - 3; 3,5
utt - (1 + t)(1 + x) uxx = cos(t x), u(x,0) = 1 - x, ut(x,0) = 0,5x, 0£ x £1, u(0,t) = cos(t), ux(1,t) + s1 u(1,t) = 2 t - 1,0£ t £1, s1 = - 2; 2,5
utt - (t + cos(p x/2)) uxx = 1 + tx, u(x,0) = x2/2, ut(x,0) = 0,3x, 0£ x £1, - ux(0,t) + s0×u(0,t) = 2 t, ux(1,t) = 0,0£ t £1, s0 = - 2,5; 2
utt - (1 + sin(p x/2)) uxx = 1 + t, u(x,0) = x2/2, ut(x,0) = 0,5, 0£ x £1, u(0,t) = 0, ux(1,t) + s1 u(1,t) = t2 + 2,0£ t £1, s1 = - 1; 2
utt - (1+ x/(1+t2)) uxx = t + x, u(x,0) = cos(p x), ut(x,0) = x/3, 0£ x £1, - ux(0,t) + s0 u(0,t) = 2 t - 1, ux(1,t) + u(1,t) = - 1,0£ t £1, s0 = - 2; 2
utt - arctg((1 + x)/(1+t2)) uxx = t x, u(x,0) = 1 - x, ut(x,0) =sin(p x), 0£ x £1, u(0,t) = 1 + t, ux(1,t) + s1 u(1,t) = t2- 1,0£ t £1, s1 = - 2; 3

Таблица 16. Варианты заданий к лабораторной работе №3

Волновая задача
utt - cos(x/(1+t)) uxx = x + t, u(x,0) = sin(p x), ut(x,0) = 0,3x, 0£ x £1, u(0,t) = 2 t, ux(1,t) + s1 u(1,t) = 0,4arctg(t - 1),0£ t £1, s1 = - 2; 1
utt - (1 + arctg(x/(1+t2))) uxx = x + t, u(x,0) = cos(p x), ut(x,0) = 0,5x, 0£ x £1, u(0,t) = t +1, ux(1,t) + s1 u(1,t) = t - 1,0£ t £1, s1 = - 0,5; 1
utt - (1 + sin2(x + t)) uxx = 1 + t, u(x,0) = cos(p x), ut(x,0) = x, 0£ x £1, - ux(0,t) + s0 u(0,t) = 2 t, u(1,t) = -1 + t, 0£ t £1, s0 = - 2; 3
utt - (1 + cos2(x + t)) uxx = e t - x, u(x,0) = ln(1 + x), ut(x,0) = x/2, 0£ x £1, - ux(0,t) + s0 u(0,t) = 1 + t, ux(1,t) = ln(2 - t),0£ t £1, s0 = - 2; 1,7
utt - (1 + t + sin2(x)) uxx = t - cos2(x), u(x,0) = x2/2, ut(x,0) = sin(x), 0£ x £1, ux(0,t) = 0, ux(1,t) + s1 u(1,t) = t +0,2,0£ t £1, s1 = - 2; 2
utt - ((1 + x)/(1 + t)) uxx = t x, u(x,0) = x sin(p x), ut(x,0) = 0,5x, 0£ x £1, - ux(0,t) + s0 u(0,t) = sin(t), u(1,t) = -2 t,0£ t £1, s0 = - 0,5; 2
utt - (1 + t + sin2(p x/2)) uxx = t x, 0£ x £1, u(x,0) = cos2(p x/2), ut(x,0) = x/2, 0£ x £1, - ux(0,t) + s0×u(0,t) = cos(t), u(1,t) = - t,0£ t £1, s0 = - 2; 1,5
utt - (x2 + t2) uxx = x + 2t, u(x,0) = 1 - x, ut(x,0) = sin(x), 0£ x £1, ux(0,t) = t -1, ux(1,t) + s1×u(1,t) = 2 t,0£ t £1, s1 = - 2; 1

 





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