1、a0a2a1a4a3a4a5a4a6a4a7a4a8a4a9a4a10a4a11a4a7 a12a14a13a14a15a17a16a14a18a14a19a14a20a21 4a22a24a23a24a25a24a26a24a27a24a28a24a29a24a30a24a31a24a32 *a33a35a34 f(t; x)a36 (t;x) a37a35a38a35a39a35a40 G a41 k a42a35a43a35a44a35a45a3a35a46 x = (t)a36a35a39a35a47a35a38 I a48a35a49a6a35a7a35a50 (E)a51a35a5
2、2a46a53a55a54a57a56 (t)a58a35a59 (E) a60a35a61a35a51a35a62a35a63a35a64a35a65a35a66a46a68a67a42a35a69a35a70 (t) a51a35a71a35a61 k + 1 a72a3a35a73a35a74a49a35a43a35a44a35a51a35a75a33a35a34 f(t; x)a36a35a40 G a41a57a76a35a77a35a42a35a43a35a44a35a45a3a35a46 a53 a6a35a7a35a50 (E)a51a35a52 x = (t) a78a35a
3、49a35a76a35a77a35a42a35a43a35a44a35a45a3a51a35a75a68a65a35a79a35a80a82a81a33a82a83a51a82a84a35a85a86a14a87a14a88 a33a14a34 f(t; x)a36a14a40 G a41a89a49a14a52a14a90a14a51a46a92a91a14a93a14a6a14a7a14a50 (E)a49a14a94a14a95a14a36a14a52a14a90a14a52a14a96a14a97a14a98a35a99a35a51a35a100a14a101a35a102a35a10
4、3a105a104a57a36a12a35a106a14a15x 7 a107a46a68a108a35a109a35a110a69a35a39a35a111a35a112a35a113a6a35a7a35a114a35a115a35a116a35a117a99a35a51a55a118a57a119a82a75a83a82a120a51a35a121a82a122a35a99a19a35a123a82a16a35a18a35a6a82a7a35a50a98a115a35a116a35a124a82a125a51a55a118a92a119a35a75a68a36a12a14a106a14a1
5、5 x 7a107a46a68a108a14a109a14a110a14a123a14a16a14a126a14a127a35a128a51a35a129a35a130a14a98a115a35a131a52a35a90a35a51a14a99a35a132a35a75a134a133a35a135a14a136a35a45a35a137a35a99a35a132a14a138a35a139a35a52a35a90a35a129a35a130a14a75a108a35a109a35a140a129a14a130F(x1; ; xm) a36a14a141 (x01; ; x0m) a51a14
6、a142a14a40 jxi x0ij 0a4a6a5a3a7a3a8a3a9 a46a11a10a3a12a3a13a15a14 (E)a1 t = a16a3a17a3a18a3a19a3a20a7a3a8a3a7 x = (t),a21a3a22a3a23a3a24a3a25a3a26 x( ) = .a27a29a28a215a29a30a29a31a29a32a46 a108a4a109a29a33a69 n = 1a51a4a199a4a200a185a4a186a4a187a75 a174a15a34a4a205 = 0; = 0. a94a53 a33a29a35a4a114a
7、4a127a29a36 t ! t ; x !x , a69a3a37a3a38a14a149a172a3a39a199a14a200a14a75a134a193a35a49a14a242a35a99a19a51a167a205a46 f(t; x)a36R : jtj :a0 = (0);a1 = ddt 0 = f(0; 0) = a00;a2 = 12d2dt20= 12df(t;(t)dt0= 12 ft 0 + fx 0 ddt 0 = 12(a10 + a01a00);. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8、 . . . . . . . . . . am = 1m!dm 1f(t;(t)dtm 10= Pm(a00; a10; a01; ; am 1;0; ; a0;m 1);. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (4.6)a54a35a162a64a35a107 Pma241a35a245a49a15a55a15a56 a41a58a57a128a51a15a50a35a99a35a51a15a59a35a227a35a130a35a138a35a159a35a64a46a146
9、a33a191a15a60a15a61 m a196a35a192a46a68a176a191a153a20a35a6a35a7a51a35a189a15a62a35a200a35a64a76a14a192a14a75a63a36a3a64a186a14a187a14a88a227a14a130a54a58a65a64 (4.6) a99a115a51a14a151a14a130 (4.5) a36a14a40C : jtj = r(1 e 12M )a41a89a156a14a157a46a147a14a233 r minf ; g. a172 a16 a141a16a3a66 a186a1
10、4a187 a46 a53a55a54a193 (4.6) a67a187 d(t)dt a191 f(t; (t) a137a3a68a146a109a51a3a57a14a72a3a73a36 t = 0 a233a14a51a14a101a74a3a69a63a46 a163a147a172a198a126a52a35a90a35a129a14a130a35a189a35a196a69a35a124a51a35a150a35a151a35a130a14a148a35a64a46a218a146a109a14a232a15a70a15a69a63a3a71a36a15a72a228a46
11、(t)a36 t = 0 a47a3a48a14a49 (E) a51a14a52a14a75a51 a54a193 (0) = 0, a73 (t) a96a14a97a14a100a14a101a14a102a14a103 (4.4).a215a116 a186a14a187a227a14a130a54a6a65a64 (4.6) a99a115a51a14a151a14a130 (4.5) a36 C a41a89a156a14a157a46a75a74 a184a121a14a122a3a76a115a51a35a190a14a151a35a130a14a240a46a78a77a3a
12、79a15a80a3a81a35a6a14a7dxdt = F(t; x); (4.7)a155a14a107 F(t;x) a49 f(t; x) a51a14a190a14a129a14a130a14a75a172 a125a51a6a14a7a214a35a215 (E) a51 a207a3a82a3a83 . a164a14a165a14a48a3a84a14a113a14a219 3, a108a14a109 a45a160F(t;x) = M(1 tr )(1 xr );a155a14a107 r minf ; g. a56 F(t;x) a148a3a85a88F(t; x)
13、=1Xi;j=0Aijtixj;a53jaijj Aij: (4.8)a54 a83a3a86 a65a64a67a42a3a50a35a99 Ai:8:A0 = 0;A1 = A00;A2 = 12(A10 + A01A00);. . . . . . . . . . . . . . . . . . . . . . . . . . . . Am = Pm(A00; A10; A01; ; Am 1;0; ; A0;m 1);. . . . . . . . . . . . . . . . . . . . . . . . . . . . (4.9)3a0a2a1a4a3a4a5a4a6a4a7a4
14、a8a4a9a4a10a4a11a4a7 a12a14a13a14a15a17a16a14a18a14a19a14a20a77a3a79a137a172 a125a99a115a51 Ai a215a14a227a14a130a14a51a14a150a14a151a14a1301Xi=0Aiti: (4.10)a54 (4.8)a213a14a48a3a84a14a113a14a219 2 a69a14a70a46 (4.10)a49 (4.5) a51a14a190a14a151a14a130a14a75 a215a116 a186a14a187 (4.5)a36 C a41a89a156
15、a14a157a46a164a14a165a14a48a3a84a14a113a14a2191, a33a3a49 a186a14a187 (4.10) a36 C a41a89a156a14a157a14a75a215a116 a186a14a187 (4.10)a36 C a41a89a156a14a157a46a87a51a3a33a3a49 a186a14a187 a80a3a81a14a6a14a7 (4.7)a36 C a41a89a196a14a96a14a97a14a100a14a101a14a102a14a103 (4.4) a51a14a52a14a90a14a52a14a
16、75a172a49a163a215a46a33a14a34 a172a16a141a35a60a35a61a116 a186a35a187 a46 a53a164a35a165a15a88a15a84a35a192a35a193a46 a16a113a35a51a186a35a187a45a35a70a46 (4.10) a16a99a14a49a172 a126a52a14a90a35a52a35a36 C a41a89a51a14a150a14a151a14a130a14a148a14a64a46a68a163a35a176 (4.10)a40a14a36 C a41a89a156a14a
17、157a14a75a172 a125a14a16 a185 a46 a86a14a87a69a127a149a116a35a16a35a126a30a3a31a6a35a7a51a35a100a14a63a15a89a5 a86a35a87a75a123a35a6a35a7 (4.7),a218a6a14a7dxdt =M(1 tr )(1 xr );a184 a5a3a90a14a127a14a128a240a14a45a14a60a14a61 Zx01 urdu =Z t0M1 r d :a91a176x x22r = rM ln(1 tr):a172 a126a192a14a193 x
18、a51a106a42a6a14a7a196a14a52(t) = r r1 + 2M ln(1 tr)12 ;a92a177 a172 a126a52a3a42 t = 0a173a215a3a93a46a68a176a36 C a41a89a49 t a51a14a52a14a90a14a129a14a130a14a75a68a99a19 a186a15a94a75 a95 a961. a186a14a187a14a88(1) a6a14a7tx0 = x ta193 t = 0 a97a14a196a14a192a14a193 t a51a14a200a14a64a14a150a14a15
19、1a14a130a3a71(2) a6a14a7t2x0 = x ta193 t = 0 a196a14a192a14a193 t a51a14a200a14a64a14a150a14a151a14a130a46a11a98 a172 a126a200a35a64a14a150a35a151a35a130a15a99a116 t = 0 a16a141a3a100a3a101a3a102a14a752. a123 (E) a49 n a103a105a104a128a14a6a14a7a14a50a51a14a199a14a200a46 a186a35a187a121a35a122a35a99a19a754
