1、a0a2a1a4a3a4a5a4a6a4a7a4a8a4a9a4a10a4a11a4a7 a12a14a13a14a15a17a16a14a18a14a6a14a7a19 5a20a22a21a22a23a22a24a22a25a22a26a22a27a22a28a29 x2a30a32a31a34a33a36a35a36a37a36a38a36a39a36a40a36a41a22a42 (NH)a43a36a44a36a45a47a46a32a48a36a31a34a49a47a50a32a39a36a51a22a43a36a52a22a53a29a22a54a36a55a22a56a36a
2、57a58a22a59 x4a43a22a60a22a61a22a31a62a33a22a35a22a63a56a65a64a65a66a65a67a31a68a44a65a45a69a46a70a48a65a43a65a52a65a71a65a72a65a73a22a40a65a41a65a42 (LH) a43a22a74a22a75a22a52a76a47a77a32a78a47a79a32a57a75a22a80a22a81a79a83a82a72a22a73a22a74a65a75a22a52a76a69a77a31a85a84a22a71a65a86a22a60a22a61a65a
3、87a22a45a69a46a70a48a22a88a65a89a22a90a22a52a57a85a91a22a92a22a93a94a31a62a33a22a35a22a95a22a60a22a61a22a96a22a97a22a98a65a99a22a87a65a45a22a100a65a101a65a43a22a87a65a45a102a46a83a48a82a89a22a90a22a87a22a45a22a100a22a101a82 x(a) = x(b),a103a22a104a87a22a45a22a100a22a101a82 Lx(a) + Nx(b) = 0,a105a30
4、a; b 2 I; L; N a91 n na106a76a47a77a32a57a108a107a44a22a45a102a46a83a48a22a109a102a110a83a31a56a22a111a22a112a22a113a31a114a87a22a45a69a46a83a48a65a109a56a115a97a22a52a22a31a62a116a22a117a22a97a22a31a62a118a22a109a56 a115 a55a65a56a22a57a119a33a22a35a22a97a22a99a22a120a22a43a22a74a22a75a22a121a65a12
5、2a57a123a22a124 5.1a125a22a126a22a127a22a128 (LH) a129a83a130a22a131a69a132a83a133a22a134a22a135a65a136a65a137a65a138 x = 0, a139a83a140a22a141a22a142 f(t), a126a127a22a128 (NH) a129a83a130a22a131a69a132a83a133a22a143a22a135a22a138a57a144a22a145 a146a22a147a22a148a89a22a90a22a87a22a45a22a100a22a101a
6、57a150a149 a115a22a151 4.2 a66a31a62a40a22a41a22a42 (NH) a43a22a52a22a71a78a22a152x = (t)c +Z ta1(s)f(s)ds: (5.1)a149a83a153a22a66a31a62a51a22a154a22a155a22a89a22a90a22a87a65a45a22a100a65a101a22a156a54a65a157a156a102a158a70a159 c a154a22a155(a)c = (b)c +Z ba1(s)f(s)ds;a116(a) (b)c = (b)Z ba1(s)f(s)d
7、s: (5.2)a160a22a161a22a162a22a163a40a22a41a22a42 (LH), (5.2) a164a152(a) (b)c = 0: (5.3)a165a36a166a36a167a31 (LH) a95a36a97a36a168a36a169a36a52a36a154a36a155a22a89a36a90a22a87a22a45a22a100a22a101a22a31a170a116a36a171a161 ca43a36a172a36a173a36a174a36a175a36a40a36a41a36a42 (5.3)a95a22a97a22a176a22a52
8、 c = 0, a177a22a178a22a97det(a) (b)6= 0;a179a22a180a71a149 (5.2)a181 c a52a79a31a62a174a22a182 (5.1) a183a22a184a22a185 (NH) a154a22a155a22a89a22a90a22a87a22a45a22a100a22a101a22a43a22a52a57a166a98a22a186a147a22a148a43a22a187a103a22a104a87a65a45a22a100a65a101a22a31a68a188a65a174a65a189 (5.2) a88 (5.3
9、) a43a22a190a22a191a22a187L (a) + N (b)c = N (b)Z ba1(s)f(s)ds1a0a2a1a4a3a4a5a4a6a4a7a4a8a4a9a4a10a4a11a4a7 a12a14a13a14a15a17a16a14a18a14a6a14a7a88 L (a) + N (b)c = 0:a105a22a192a110a151 a57 a115a22a151a49a22a193a57a194 5.1a195a22a196a22a197 5.1 a129a83a198a69a199a83a200a22a201a82a68a202a65a203a126
10、a65a127a204a128 (LH) a205a83a135a22a206a22a138 x = 0 a207a22a208a22a209a210a130a22a131a69a211a83a212 (a213a83a214a22a130a22a131a69a211a83a212 ) a129a22a215a83a216a69a211a83a212a22a217 (b) (a)(L (a) + N (b) a217a69a218a83a219a220a22a221a69a222 a57a99a36a120a36a60a36a61a36a40a36a41a36a42 (NH)a43a36a89
11、a36a90a36a52a57a33a36a35a22a43a69a46a83a48a22a187a82a98a22a122 A(t)a88 f(t)a223a29 R1a224a97a115a36a225a31a227a226a54a187 !-a89a36a90a36a228a36a175a36a31a85a116a65a86 ! a91 a89a36a90a36a43a36a89a22a90a65a228a22a175a22a31a230a229a22a231 ! 0 a91a36a232 a106a175a22a31a62a233a22a234a29a22a235a204a236a10
12、0a204a101a65a99a65a31a68a40a204a41a65a42 (NH) a53a29 !-a89a22a90a22a52a238a237a114a99a22a239a241a240a22a242a22a243 (Massera,1915-2002)a244a22a245a247a246a79a39a69a248a83a249a57a123a22a124 5.2a125 A(t) a250 f(t) a251 R1 a252 a135a22a196a22a253a22a31a204a254a83a255a22a217 !- a209a210a1a0a1a2a31a204a13
13、9a83a126a22a127a65a128(NH) a3a22a251 !- a209a210a138a69a129a22a215a83a216a69a211a83a212a22a217a82 (NH)a135a1a4a1a5a22a251 R1 a252 a135a1a6a69a129a83a138 a57a144a36a145a178a8a7a36a173a36a187a8a9a8a10a36a43a57a95a1a11a22a49a47a50a13a12a22a190a22a173a57a14a167 x = x0(t)a187 (NH)a161 R1 a224a97a14a43a36
14、a52a57a32a149 A(t)a88 f(t)a43a36a89a36a90a36a173a66a31a160a1a15 a235a1a16a1a17a175 k; x0(t + (k 1)!)a187 (NH)a154a22a155a22a44a22a45a22a100a22a101 x(0) = x0(k 1)!) a43a22a52a22a31a62a177a149 (4.5)a97x0(t + (k 1)!) = (t)x0(k 1)!) +Z t01(s)f(s)ds; k = 1; 2; ;a105a30 (t) a187 (LH) a43a1a18a1a19a1a20a1a
15、21a76a69a77a31a23a22a22a191a25a24a22a97x0(k!) = (!)x0(k 1)!) + v; k = 1; 2; ; (5.4)a105a30 v = (!) R !0 1(s)f(s)ds.(NH) a43 a15 a235 a52a22a223a22a71 a149 (4.2) a78a69a79 a31a62a51a22a187 !- a89a22a90a22a52a22a31a62a156a54a22a157a156(0)c = (!)c +Z !01(s)f(s)ds:a26a1a27a185 (0) = E, a224a1a28 a24a22a
16、71a1a29a152( (!) E)c = v: (5.5)a166a98 (NH) a30a22a97 !- a89a22a90a22a52a22a31a62a188a22a171a161 ca43a22a172a22a173a22a174a22a175a22a40a22a41a65a42 (5.5) a178a1a31a22a52a57a204a149a172a22a173a174a22a175a22a43a66a1a32a33a22a35a66a22a67a31a62a178a65a53a29a1a33a176a102a158a83a159 u, a117a22a184u( (!) E
17、) = 0; (5.6)uv 6= 0; (5.7)2a0a2a1a4a3a4a5a4a6a4a7a4a8a4a9a4a10a4a11a4a7 a12a14a13a14a15a17a16a14a18a14a6a14a7a34a1a35 (5.4), (5.6)a71a22a86a22a49a69a50ux0(k!) = ux0(0) + kuv; k = 1; 2; ; (5.8)a119 a149 a161a97 (5.7), a180 x0(t) a36a22a187a22a97a14a43a22a31a62a156 k a12a22a190a1a37a1a38 (5.8) a109a22
18、a71a1a39a152a1a40a31a62a229a56a25a41a42a24a78a50 (NH) a178a22a97 !- a89a22a90a22a52a57a43 a29a248a13a44a112a69a149 (5.4), (5.6)a45a1a46 (5.8). a166a22a167 a156 k = m a38 (5.8) a152a1a40a22a57 a72a22a73a22a156k = m + 1 a38a22a43 (5.4) a71a22a184ux0(m + 1)!) = u (!)x0(m!) + uv= u( (!) E)x0(m!) + ux0(m
19、!) + uv= ux0(0) + muv + uv= ux0(0) + (m + 1)uv;a177a22a156 k = m + 1 a38a22a31 (5.8) a118a152a1a40a22a57a72a22a73a65a156 k = 1 a38a22a43 (5.4) a47a1a48a1a49a22a49a22a156 k = 1a38a22a31 (5.8) a118a152a1a40a22a57a23a50a1a51a31 (5.8) a160a1a15 a235a1a16a1a17 a175 k a223a152a1a40a22a57a23a52a22a153a31a1
20、15a65a151a184a65a185a65a39a65a193a53a43a22a49a69a50a57a54a241. a167 I = R1; ! 0, a54a36a29 I a224 a31 A(t + !) A(t); f(t + !) f(t). a49a47a50a82a56a55a160 (LH)a43a1a57a56a52 x = x(t), a97limt!+1x(t) = 0;a188 (NH) a97a55a204a56a43 !- a89a204a90a204a52 x = x0(t), a226a54 (NH)a43a105a51a204a52 x = x(t)
21、 a156t ! +1a38a22a223a1a58a1a59a161a51a22a31a62a116limt!+1(x(t) x0(t) = 0:2. a49a69a50a26 5.1.3. a49a47a50a82 (NH)a97a55a36a56a52 x = x(t) a154a36a155a36a87a36a45a36a100a22a101 B(x) kPi=1Lix(ti) = 0 a43a12a1a7a22a100a22a101a22a187 (LH) a95a22a97a22a168a22a169a22a52 x = 0 a154a22a155a22a87a22a45a22a1
22、00a22a101 B(x) = 0, a116a76a69a77kPi=1Li (ti)a33a8a60a8a61a31a105a30 Li; i = 1; ; k a187 n a62a76a47a77a31 ti 2 I; (t)a187 (LH)a43a36a74a36a75a36a52a76a47a77a32a574. a49a69a50a82 (NH)a97a55a22a56a52 x = x(t) a154a22a155a22a87a22a45a22a100a22a101 B(x) R ba x(s)ds = 0 a43a12a1a7a22a100a22a101a22a187 (LH) a95a22a97a22a168a22a169a22a52 x = 0 a154a22a155a22a87a22a45a22a100a22a101 B(x) = 0, a116a76a69a77 R ba (s)dsa33a1a60a1a61a31a105a30 (t) a187 (LH) a43a22a74a22a75a22a52a76a69a77a83a573
