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Tables of Contents for Generalized Quasilinearization for Nonlinear Problems
Chapter/Section Title
Page #
Page Count
Preface
vii
1. FIRST ORDER DIFFERENTIAL EQUATIONS
1
68
1.0 Introduction
1
1
1.1 Method of upper and lower solutions
2
8
1.2 Method of quasilinearization
10
5
1.3 Extensions
15
15
1.4 Generalizations
30
22
1.5 Refinements
52
15
1.6 Notes
67
2
2. FIRST ORDER DIFFERENTIAL EQUATIONS (CONT.)
69
112
2.0 Introduction
69
1
2.1 Periodic boundary value problems
70
25
2.2 Anti-periodic boundary value problems
95
18
2.3 Interval analysis and quasilinearization
113
19
2.4 Higher order convergence
132
6
2.5 Another refinement of quasilinearization
138
22
2.6 Extension to system of differential equations
160
19
2.7 Notes
179
2
3. SECOND ORDER DIFFERENTIAL EQUATIONS
181
40
3.0 Introduction
181
1
3.1 Method of upper and lower solutions.
182
4
3.2 Extension of quasilinearization
186
5
3.3 Generalized quasilinearization
191
6
3.4 General second order BVP
197
12
3.5 General second order BVP (continued)
209
5
3.6 Higher order convergence
214
6
3.7 Notes
220
1
4. MISCELLANEOUS EXTENSIONS
221
48
4.0 Introduction
221
1
4.1 Dynamic systems on time scales
222
7
4.2 Integro-differential equations
229
8
4.3 Functional differential equations
237
7
4.4 Impulsive differential equations
244
9
4.5 Stochastic differential equations
253
9
4.6 Differential equations in a Banach space
262
5
4.7 Notes
267
2
References
269
6
Index
275