Контрольные работы по уравнениям математической физики. Ковтанюк А.Е. - 18 стр.

UptoLike

ВУЗ: 

ДВФУ | Владивосток

Составители: 

Рубрика: 

39. u
t
= a
2
u
xx
+ 3t
2
, 0 < x < 1, t > 0,
u(0, t) = t
3
, u(1, t) = 1,
u(x, 0) = x − 2sinπx + 3sin2πx.
40. u
t
= a
2
u
xx
+ 3(x − 1), 0 < x < 1, t > 0,
u
x
(0, t) = 3t, u(1, t) = 2t
3
,
u(x, 0) = cos
π
2
x − cos
3π
2
x.
41. u
t
= a
2
u
xx
+ 4xt
2
, 0 < x < 1, t > 0,
u(0, t) = 2, u
x
(1, t) = 2t
3
,
u(x, 0) = 2 − sin
9π
2
x.
42. u
t
= u
xx
+ t + 2, 0 < x < 1, t > 0,
u
x
(0, t) = 1, u
x
(1, t) = −1,
u(x, 0) = 1 + x − x
2
+ cos2πx − cos3πx.
43. u
t
= a
2
u
xx
− 3xt
2
+ 2x, 0 < x < 1, t > 0,
u(0, t) = t
3
, u(1, t) = 2t,
u(x, 0) = 3sin2πx − sin5πx.
44. u
t
= a
2
u
xx
+ t
2
, 0 < x < 1, t > 0,
u
x
(0, t) = 1, u(1, t) = t
3
,
u(x, 0) = x − 1 + cos
7π
2
x.
45. u
t
= a
2
u
xx
+ 4x, 0 < x < 1, t > 0,
u(0, t) = t
3
, u
x
(1, t) = 4t,
u(x, 0) = 3sin
π
2
x − sin
7π
2
x.
46. u
t
= u
xx
+ t
2
− 3, 0 < x < 1, t > 0,
u
x
(0, t) = 0, u
x
(1, t) = 4,
u(x, 0) = 1 + 2x
2
+ 3cos5πx.
47. u
t
= a
2
u
xx
+ 4(1 − x), 0 < x < 1, t > 0,
u(0, t) = 4t, u(1, t) = t
3
,
u(x, 0) = sin2πx − 2sin3πx.
48. u
t
= a
2
u
xx
+ 3xt
2
, 0 < x < 1, t > 0,
u
x
(0, t) = t
3
, u(1, t) = 2t,
u(x, 0) = 5cos
π
2
x − 2cos
5π
2
x.
49. u
t
= a
2
u
xx
+ 2t
2
, 0 < x < 1, t > 0,
u(0, t) = 2t
3
, u
x
(1, t) = 1,
u(x, 0) = x − 2sin
3π
2
x.
50. u
t
= u
xx
+ 2t − 1, 0 < x < 1, t > 0,
u
x
(0, t) = 1, u
x
(1, t) = 5,
u(x, 0) = 3 + x + 2x
2
+ 2cosπx − cos3πx.
18
39. ut = a2 uxx + 3t2 , 0 < x < 1, t > 0,
    u(0, t) = t3 , u(1, t) = 1,
    u(x, 0) = x − 2sinπx + 3sin2πx.

40. ut = a2 uxx + 3(x − 1), 0 < x < 1, t > 0,
    ux (0, t) = 3t, u(1, t) = 2t3 ,
    u(x, 0) = cos π2 x − cos 3π
                              2
                                x.

41. ut = a2 uxx + 4xt2 , 0 < x < 1, t > 0,
    u(0, t) = 2, ux (1, t) = 2t3 ,
    u(x, 0) = 2 − sin 9π 2
                           x.

42. ut = uxx + t + 2, 0 < x < 1, t > 0,
    ux (0, t) = 1, ux (1, t) = −1,
    u(x, 0) = 1 + x − x2 + cos2πx − cos3πx.

43. ut = a2 uxx − 3xt2 + 2x, 0 < x < 1, t > 0,
    u(0, t) = t3 , u(1, t) = 2t,
    u(x, 0) = 3sin2πx − sin5πx.

44. ut = a2 uxx + t2 , 0 < x < 1, t > 0,
    ux (0, t) = 1, u(1, t) = t3 ,
    u(x, 0) = x − 1 + cos 7π 2
                               x.

45. ut = a2 uxx + 4x, 0 < x < 1, t > 0,
    u(0, t) = t3 , ux (1, t) = 4t,
    u(x, 0) = 3sin π2 x − sin 7π2
                                   x.

46. ut = uxx + t2 − 3, 0 < x < 1, t > 0,
    ux (0, t) = 0, ux (1, t) = 4,
    u(x, 0) = 1 + 2x2 + 3cos5πx.

47. ut = a2 uxx + 4(1 − x), 0 < x < 1, t > 0,
    u(0, t) = 4t, u(1, t) = t3 ,
    u(x, 0) = sin2πx − 2sin3πx.

48. ut = a2 uxx + 3xt2 , 0 < x < 1, t > 0,
    ux (0, t) = t3 , u(1, t) = 2t,
    u(x, 0) = 5cos π2 x − 2cos 5π2
                                   x.

49. ut = a2 uxx + 2t2 , 0 < x < 1, t > 0,
    u(0, t) = 2t3 , ux (1, t) = 1,
    u(x, 0) = x − 2sin 3π  2
                             x.

50. ut = uxx + 2t − 1, 0 < x < 1, t > 0,
    ux (0, t) = 1, ux (1, t) = 5,
    u(x, 0) = 3 + x + 2x2 + 2cosπx − cos3πx.




                                             18

Страницы