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: , . Y(t), (t) = const. v(t) , , , . :
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. , C(0) = Y(0) , , .
3) , , .. :
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|
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, . (19) , , . , , . .
3) , Y(0) = C(0).
, (20), a0 = 0. , - r . (19) , Y(0) t, .. Y(t) = Y(0) = const. r, :
, (21)
k , :Y(0) = C(0) .
, - , .
1.
1
B | Y(0) | C(0) 1 | C(0) 2 | C(0) 3 |
1. .
2. Excel, (9) Y = f1(t) , .. C(t) = 0. Y(0) . t 0 20 Dt = 1 . 2.
2
Y(t) = f1(t) |
359,5271 |
461,642 |
592,76 |
761,1189 |
977,296 |
1254,873 |
1611,289 |
2068,936 |
2656,566 |
3411,098 |
4379,937 |
5623,95 |
7221,295 |
9272,327 |
11905,9 |
15287,48 |
19629,52 |
25204,8 |
32363,6 |
41555,68 |
, " " Excel, Y = f1(t) ( 1).
Y = f1(t) , , . (1/4). () .
3. Y = f(t) (13) C(0) , .. C(t) = C(0) = const. C(0) 1.
3.
3
Y(t) = f2(t) | Y(t) = f3(t) | Y(t) = f4(t) |
331,1246 | 316,9233 | |
396,7698 | 364,33377 | |
481,06 | 425,21 | |
589,2907 | 503,37664 | |
728,2617 | 603,74458 | |
906,704 | 732,61958 | |
1135,828 | 898,09835 | |
1430,03 | 1110,5773 | |
1807,792 | 1383,4057 | |
2292,849 | 1733,7242 | |
2915,674 | 2183,5421 | |
3715,397 | 2761,1198 | |
4742,261 | 3502,7442 | |
6060,781 | 4455,0088 | |
7753,795 | 5677,7407 | |
9927,667 | 7247,7595 | |
12718,97 | 9263,7036 | |
16303,08 | 11852,227 | |
20905,17 | 15175,957 | |
26814,37 | 19443,711 |
" " Excel, : Y = f2(t), Y = f3(t), Y = f4(t), = f5(t), = f6(t), = f7(t) ( 2).
|
|
Y = f2(t) = f5(t), Y = f3(t) = f6(t) , Y(t), C(t) = const. v(t) , , , . , Y = f2(t), Y = f3(t), = f5(t), = f6(t) Y = f1(t) .
, C(0) = Y(0) , , .
4. , :
(22)
r C(0) :
(23)
B, Y(0) C(0) .
:
r1 | r2 | r3 |
0,16 | 0,12 |
5. r = f8(t), = f9(t), = f10(t), (22), Y = f11(t), Y = f12(t), Y = f13(t), (19). t 0 30 Dt = 1 .
:
4
C = f8(t) | C = f9(t) | C = f10(t) | Y = f11(t) | Y = f12(t) | Y = f13(t) |
117,4349 | 168,4614 | 328,8178 | 314,4613 | ||
137,9096 | 189,195 | 386,147 | 353,164 | ||
161,9541 | 212,4804 | 453,4715 | 396,63 | ||
190,1907 | 238,6316 | 532,534 | 445,4457 | ||
223,3503 | 268,0015 | 625,381 | 500,2694 | ||
262,2913 | 300,986 | 734,4158 | 561,8406 | ||
308,0217 | 338,0302 | 862,4607 | 630,9897 | ||
361,7251 | 379,6337 | 1012,83 | 708,6495 | ||
424,7916 | 426,3575 | 1189,417 | 795,8673 | ||
498,8538 | 478,8319 | 1396,791 | 893,8195 | ||
585,8286 | 537,7646 | 1640,32 | 1003,827 | ||
687,9675 | 603,9506 | 1926,309 | 1127,374 | ||
807,9142 | 678,2825 | 2262,16 | 1266,127 | ||
948,7736 | 761,7629 | 2656,566 | 1421,957 | ||
1114,192 | 855,5176 | 3119,737 | 1596,966 | ||
1308,45 | 960,8114 | 3663,661 | 1793,515 | ||
1536,578 | 1079,064 | 4302,418 | 2014,253 | ||
1804,479 | 1211,871 | 5052,542 | 2262,16 | ||
2119,089 | 1361,024 | 5933,45 | 2540,578 | ||
2488,551 | 1528,533 | 6967,943 | 2853,262 | ||
2922,428 | 1716,659 | 8182,799 | 3204,43 | ||
3431,952 | 1927,939 | 9609,466 | 3598,819 | ||
4030,311 | 2165,222 | 11284,87 | 4041,748 | ||
4732,993 | 2431,709 | 13252,38 | 4539,19 | ||
5558,187 | 2730,994 | 15562,92 | 5097,856 | ||
6527,254 | 3067,114 | 18276,31 | 5725,28 | ||
7665,277 | 3444,603 | 21462,77 | 6429,925 | ||
9001,713 | 3868,551 | 25204,8 | 7221,295 | ||
10571,16 | 4344,677 | 29599,24 | 8110,064 | ||
12414,23 | 4879,403 | 34759,85 | 9108,219 |
" " Excel, : = f8(t), = f9(t), = f10(t), Y = f11(t), Y = f12(t), Y = f13(t) ( 3).
= f8(t) Y = f11(t) [ = f9(t) Y = f12(t)], = 0,07 [ =0,12], r < 1/B (0,16 < 0,25 [0,12 < 0,25]), , . , . , , -.
|
|
= f10(t) Y = f13(t) , Y(0) = C(0), (20), a0 = 0. , - r . (19) , Y(0) t, .. Y(t) = Y(0) = const.
6. C(t) C(0) :
. (24)
:
r1 | r2 | r3 |
0,2 | 0,15 |
7. (22) (19), r, : = f14(t), = f15(t), = f16(t), Y = f17(t), Y = f18(t), Y = f19(t) ( 4). 5.
5
C = f14(t) | C = f15(t) | C = f16(t) | Y = f17(t) | Y = f18(t) | Y = f19(t) |
122,2494 | 173,4214 | 328,2019 | 313,8159 | ||
149,4491 | 200,4999 | 383,1248 | 350,0989 | ||
182,7006 | 231,8065 | 445,1267 | 388,4352 | ||
223,3503 | 268,0015 | 514,3227 | 428,1195 | ||
273,0444 | 309,848 | 590,4384 | 468,0452 | ||
333,7951 | 358,2285 | 672,6063 | 506,5583 | ||
408,0624 | 414,1633 | 759,0816 | 541,2667 | ||
498,8538 | 478,8319 | 846,8537 | 568,7874 | ||
609,8457 | 553,598 | 931,1148 | 584,4175 | ||
745,5325 | 640,0384 | 1004,54 | 581,7026 | ||
911,4089 | 739,9758 | 1056,315 | 551,8746 | ||
1114,192 | 855,5176 | 1070,835 | 483,1196 | ||
1362,092 | 989,1006 | 1025,956 | 359,6261 | ||
1665,149 | 1143,541 | 890,6757 | 160,349 | ||
2035,635 | 1322,097 | 622,0389 | -142,592 | ||
2488,551 | 1528,533 | 161,0472 | -585,99 | ||
3042,238 | 1767,203 | -572,755 | -1218,23 | ||
3719,117 | 2043,139 | -1688,42 | -2102,78 | ||
4546,598 | 2362,16 | -3332,99 | -3322,66 | ||
5558,187 | 2730,994 | -5703,88 | -4986,22 | ||
6794,85 | 3157,419 | -9065,04 | -7234,69 | ||
8306,661 | 3650,428 | -13768,2 | -10251,7 | ||
10154,84 | 4220,416 | -20280,8 | -14275,9 | ||
12414,23 | 4879,403 | -29222,1 | -19616,8 | ||
15176,32 | 5641,287 | -41410,8 | -26675,4 | ||
18552,96 | 6522,133 | -57926,5 | -35971 | ||
22680,87 | 7540,517 | -80190,8 | -48175,2 | ||
27727,23 | 8717,914 | -110072 | -64156,1 | ||
33896,36 | 10079,15 | -150021 | -85034,8 | ||
41438,09 | 11652,94 | -203249 | -112258 |
= f14(t) Y = f17(t) [ = f15(t) Y = f18(t)], (0,25 > 0,2 > 0,16 [0,25 > 0,15 > 0,12]), , . (19) , , . , , . .
= f16(t) Y = f19(t) , Y(0) = C(0), r, (21), (20), a0 = 0. , - r . (19) , Y(0) t, .. Y(t) = Y(0) = const.
8. , , .. 0,5, (22) = f20(t), = f21(t), = f22(t) (19) Y = f23(t), Y = f24(t), Y = f25(t), t 0 30 Dt = 1 . 6 :
6
C = f20(t) | C = f21(t) | C = f22(t) | Y = f23(t) | Y = f24(t) | Y = f25(t) |
164,87213 | 247,30819 | 461,64196 | 323,057531 | 304,822739 | 257,412278 |
271,82818 | 407,74227 | 761,11891 | 354,6859 | 301,207872 | 162,165 |
448,16891 | 672,25336 | 1254,8729 | 356,291099 | 238,056647 | -69,35293 |
738,90561 | 1108,3584 | 2068,9357 | 294,041485 | 60,5027714 | -546,69788 |
1218,2494 | 1827,3741 | 3411,0983 | 108,080928 | -326,52662 | -1456,5063 |
2008,5537 | 3012,8305 | 5623,9503 | -305,51185 | -1085,7042 | -3114,2045 |
3311,5452 | 4967,3178 | 9272,3265 | -1124,7962 | -2492,8386 | -6049,749 |
5459,815 | 8189,7225 | 15287,482 | -2651,9737 | -5012,4284 | -11149,611 |
9001,7131 | 13502,57 | 25204,797 | -5396,3735 | -9422,8433 | -19891,665 |
14841,316 | 22261,974 | 41555,685 | -10211,968 | -17023,501 | -34733,488 |
24469,193 | 36703,79 | 68513,741 | -18524,993 | -29977,458 | -59753,867 |
40342,879 | 60514,319 | 112960,06 | -32710,375 | -51877,538 | -101712,16 |
66514,163 | 99771,245 | 186239,66 | -56713,834 | -88681,399 | -171797,07 |
109663,32 | 164494,97 | 307057,28 | -97079,444 | -150255,33 | -288512,63 |
180804,24 | 271206,36 | 506251,88 | -164646,23 | -252922,3 | -482440,07 |
298095,8 | 447143,7 | 834668,24 | -277348,5 | -423666,49 | -804093,27 |
491476,88 | 737215,33 | 1376135,3 | -464836,83 | -707070 | -1336876,2 |
810308,39 | 1215462,6 | 2268863,5 | -776101,88 | -1176755,2 | -2218453,9 |
1335972,7 | 3740723,5 | -1292050,7 | -1954257,8 | -3675996,3 | |
2202646,6 | 3303969,9 | 6167410,4 | -2146249,6 | -3240152,2 | -6084299,1 |
3631550,3 | 5447325,4 | -3559135,1 | -5365381,9 | -10061624 | |
5987414,2 | 8981121,3 | -5894431,2 | -8875903,7 | -16627732 | |
9871577,1 | -9752184,7 | -14672264 | -27464469 | ||
-16122176 | -24239744 | -45345421 | |||
-26636884 | -40027847 | -74844353 | |||
-43988585 | -66075998 | -123503270 | |||
-72617095 | -109045210 | -203758311 | |||
-119843708 | -179919090 | -336115085 | |||
-197740847 | -296808404 | -554384055 | |||
-326214681 | -489575148 | -914312361 |
" " Excel, ( 5).
|
|
= f20(t) Y = f23(t), = f21(t) Y = f24(t), = f22(t) Y = f25(t) , ( ), , , . (19) . , , , , , , .
, .
, , , .
1. .. - :- , 2005.
2. .., .. - .
3. . : . . .: -, 1999. XIV, 402 .
4. .. : .: , 2001. 344 .: .
5. , EXCEL ., 2000, 245 .
6. .. . . .: , 1998. 248 .
7. .. : . . . 1. : , 2005. 51 .
8. - : . / .. , .. , .. .; . .. . .:
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