Ordinary Difference-differential Equations

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University of California Press, 1958 - 262 頁
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內容

METHODS OF SOLUTION 1 Introduction
1
Integral Transformations
3
a The Laplace Transformation
4
b The Fourier Transformation c The EulerLaplace Transformation
11
The Method of Generating Functions
15
Integral Representations
19
a The LaplaceStieltjes Representation
20
b The Power Series Representation
21
The Equation yfU yit + ykit wkt
139
The Equation y?U y+1U tU
142
The Equation yU + yt ykJt 2ykt + yiti wkt
143
The Equation P d2dt2ykt 4y+1U + B4y4t + CkykM
147
FURTHER DIFFERENCEDIFFERENTIAL EQUATIONS PROBLEMS
153
A Net Problem
154
Diffusion in a Net
157
The Reduction of Functional Equations to Difference Differential Equations
159

Iterative Methods
23
SYSTEMS OF MIXED INTEGIIODIFFERENTIAL AND DIFFERENCEDIFFERENTIAL EQUATIONS WITII CONSTANT COEFFICIENTS 1 Intr...
25
Boundary Conditions
26
Other Conditions 4 The General Expansion Theorems
28
Proof of the General Expansion Theorems
31
A Boundedness Theorem
38
CHARACTERISTIC EQUATIONS 1 Introduction
41
The Asymptotic Roots of the Characteristic Equation 3
53
Direct Solution of the Characteristic Equation
56
Numerical Computation of the Characteristic Roots
59
Cauchys Index Theorem
61
x lcRoot Plateaus in Parameter Space
64
Selecting the Parameters for Maximum Damping
67
FIRST ORDER MIXED DIFFERENCE
71
Another Damping Problem
88
VARIOUS MIXED DIFFERENCEDIFFERENTIAL
111
VARIOUS DIFFERENCEDIFFERENTIAL
127
The Equation 2yt yk+lU JkM + 2Ay wkt
133
The Equation yt ykt + ykt wkt
137
A Geometric Problem
162
NONLINEAR MIXED DIFFERENCE DIFFERENTIAL EQUATIONS
165
The Basic Expansion
167
Bounded Solutions
169
Expansion of the Function fY t
171
The Trend Equations
174
The Trend Functions
175
The Solution
178
Small Changes in the Characteristic Equation
180
How to Solve Equations
182
ILLUSTRATIVE NONLINEAR DIFFERENTIAL AND MIXED DIFFERENCEDIFFERENTIAL EQUATIONS PROBLEMS
185
Van der Pols Equation
187
The Equation yt + byt 1 eyt 1
188
The Equation yt + 2ryt + co2yt f yt
194
MINORSKYS EQUATION
201
APPENDIX A EXISTENCE AND UNIQUENESS TIIEOREMS
225
APPENDIX B MISCELLANEOUS RESULTS
239
INDEX OF SYMBOLS
257
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