Контрольные работы по уравнениям математической физики. Ковтанюк А.Е. - 17 стр.

UptoLike

ВУЗ: 

ДВФУ | Владивосток

Составители: 

Рубрика: 

27. u
t
= a
2
u
xx
+ 4xt, 0 < x < 1, t > 0,
u(0, t) = 3, u(1, t) = t
2
,
u(x, 0) = 3 − 3x + 2sinπx.
28. u
t
= a
2
u
xx
+ 4xt + 1, 0 < x < 1, t > 0,
u
x
(0, t) = 2t
2
, u(1, t) = t,
u(x, 0) = cos
5π
2
x − cos
7π
2
x.
29. u
t
= a
2
u
xx
+ 6t, 0 < x < 1, t > 0,
u(0, t) = 4t
2
, u
x
(1, t) = 1,
u(x, 0) = x + 4sin
3π
2
x.
30. u
t
= u
xx
+ t − 2, 0 < x < 1, t > 0,
u
x
(0, t) = 1, u
x
(1, t) = 3,
u(x, 0) = 3 + x + x
2
− 2cos4πx.
31. u
t
= a
2
u
xx
− 2x(t − 2), 0 < x < 1, t > 0,
u(0, t) = t
2
, u(1, t) = 4t,
u(x, 0) = 4sin3πx − 3sin5πx.
32. u
t
= a
2
u
xx
+ x − 1, 0 < x < 1, t > 0,
u
x
(0, t) = t, u(1, t) = 2t
2
,
u(x, 0) = 2cos
3π
2
x − cos
9π
2
x.
33. u
t
= a
2
u
xx
+ 1, 0 < x < 1, t > 0,
u(0, t) = t, u
x
(1, t) = t
2
,
u(x, 0) = 3sin
π
2
x − sin
11π
2
x.
34. u
t
= u
xx
+ 2xt
2
, 0 < x < 1, t > 0,
u
x
(0, t) = 1, u
x
(1, t) = 1,
u(x, 0) = 1 + x − 3cos2πx + cos5πx.
35. u
t
= a
2
u
xx
+ xt
2
, 0 < x < 1, t > 0,
u(0, t) = 2, u(1, t) = t
3
,
u(x, 0) = 2 − 2x − sin5πx.
36. u
t
= a
2
u
xx
+ 6xt
2
, 0 < x < 1, t > 0,
u
x
(0, t) = 2t
3
, u(1, t) = 1,
u(x, 0) = 1 + cos
3π
2
x + cos
7π
2
x.
37. u
t
= a
2
u
xx
+ 2, 0 < x < 1, t > 0,
u(0, t) = 2t, u
x
(1, t) = t
3
,
u(x, 0) = sin
3π
2
x − 2sin
7π
2
x.
38. u
t
= u
xx
+ t + 1, 0 < x < 1, t > 0,
u
x
(0, t) = −1, u
x
(1, t) = 1,
u(x, 0) = 2 − x + x
2
− 3cos4πx.
17
27. ut = a2 uxx + 4xt, 0 < x < 1, t > 0,
    u(0, t) = 3, u(1, t) = t2 ,
    u(x, 0) = 3 − 3x + 2sinπx.

28. ut = a2 uxx + 4xt + 1, 0 < x < 1, t > 0,
    ux (0, t) = 2t2 , u(1, t) = t,
    u(x, 0) = cos 5π 2
                       x − cos 7π
                                2
                                  x.

29. ut = a2 uxx + 6t, 0 < x < 1, t > 0,
    u(0, t) = 4t2 , ux (1, t) = 1,
    u(x, 0) = x + 4sin 3π  2
                             x.

30. ut = uxx + t − 2, 0 < x < 1, t > 0,
    ux (0, t) = 1, ux (1, t) = 3,
    u(x, 0) = 3 + x + x2 − 2cos4πx.

31. ut = a2 uxx − 2x(t − 2), 0 < x < 1, t > 0,
    u(0, t) = t2 , u(1, t) = 4t,
    u(x, 0) = 4sin3πx − 3sin5πx.

32. ut = a2 uxx + x − 1, 0 < x < 1, t > 0,
    ux (0, t) = t, u(1, t) = 2t2 ,
    u(x, 0) = 2cos 3π2
                       x − cos 9π
                                2
                                   x.

33. ut = a2 uxx + 1, 0 < x < 1, t > 0,
    u(0, t) = t, ux (1, t) = t2 ,
    u(x, 0) = 3sin π2 x − sin 11π 2
                                    x.

34. ut = uxx + 2xt2 , 0 < x < 1, t > 0,
    ux (0, t) = 1, ux (1, t) = 1,
    u(x, 0) = 1 + x − 3cos2πx + cos5πx.

35. ut = a2 uxx + xt2 , 0 < x < 1, t > 0,
    u(0, t) = 2, u(1, t) = t3 ,
    u(x, 0) = 2 − 2x − sin5πx.

36. ut = a2 uxx + 6xt2 , 0 < x < 1, t > 0,
    ux (0, t) = 2t3 , u(1, t) = 1,
    u(x, 0) = 1 + cos 3π 2
                           x + cos 7π
                                    2
                                      x.

37. ut = a2 uxx + 2, 0 < x < 1, t > 0,
    u(0, t) = 2t, ux (1, t) = t3 ,
    u(x, 0) = sin 3π
                   2
                     x − 2sin 7π 2
                                   x.

38. ut = uxx + t + 1, 0 < x < 1, t > 0,
    ux (0, t) = −1, ux (1, t) = 1,
    u(x, 0) = 2 − x + x2 − 3cos4πx.




                                             17

Страницы