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Nonlinear Numerical Analysis in Reproducing Kernel Space [Hardback]

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  • Formāts: Hardback, 226 pages, height x width: 180x260 mm, weight: 666 g, Illustrations
  • Izdošanas datums: 01-Apr-2009
  • Izdevniecība: Nova Science Publishers Inc
  • ISBN-10: 1604564687
  • ISBN-13: 9781604564686
Citas grāmatas par šo tēmu:
Nonlinear Numerical Analysis in Reproducing Kernel SpacePalielināt
  • Formāts: Hardback, 226 pages, height x width: 180x260 mm, weight: 666 g, Illustrations
  • Izdošanas datums: 01-Apr-2009
  • Izdevniecība: Nova Science Publishers Inc
  • ISBN-10: 1604564687
  • ISBN-13: 9781604564686
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781604564686.html
Keywords:
Two professors of mathematics at the Harbin Institute of Technology in China introduce reproducing kernel construction theory and apply the reproducing kernel method to solving nonlinear integral equations, differential equations, and operator equations. Numerous examples demonstrate third-order obstacle problems, third-order singularity perturbed problems, Volterra-Fredholm integral equations, an age-structured population model, a damped Klein-Gordon equation, and coefficient inverse problems. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)
Foreword ix
I 1
1(74)
Fundamental Concepts of Reproducing Kernel Space
3(22)
Definition of Reproducing Kernel Space
3(1)
Fundamental Properties of Reproducing Kernel
4(1)
Reproducing Kernel Space Wm2[ a, b] and its Reproducing Kernel Function
5(12)
Absolutely Continuous Function and Some Properties
5(1)
Function Space Wm2[ a, b] is a Hilbert Space
6(2)
Function Space Wm2[ a, b] is a Reproducing Kernel Space
8(5)
Closed Subspaces of the Reproducing Kernel Space Wm2[ a, b]
13(2)
Two Notes About Reproducing Kernel Space Wm2[ a, b]
15(2)
Several Expressions of the Reproducing Kernel of Wm2[ 0,1] or Wm2[ 0, 1]
17(1)
The Binary Reproducing Kernel Space W2(m, n)(D)
18(5)
The Binary Completely Continuous Functions and Some Properties
18(2)
The Binary Function Space W(m, n)(D) is a Hilbert space
20(2)
The Binary Function Space W2(m, n)(D) is a Reproducing Kernel Space
22(1)
The Reproducing Kernel Space W2(m, n)
23(2)
Some Linear Problems
25(28)
Solving Singular Boundary Value Problems
25(5)
Introduction
25(1)
The Reproducing Kernel Spaces
26(1)
Primary Theorem and the Method of Solving Eq. (2.1.1)
27(1)
The Structure of Solution to Operator Eq. (2.1.3)
28(1)
Numerical experiments
28(2)
Solving the third-order obstacle problems
30(5)
Introduction
30(1)
Reproducing Kernel Space W32[ 0,1]
31(1)
A bounded linear operator on W32[ 0, 1]
31(2)
To Solve Eq. (2.2.5)
33(1)
Numerical Experiments
34(1)
Solving Third-Order Singularly Perturbed Problems
35(8)
Introduction
35(2)
Asymptotic Expansion Approximation
37(1)
Several Reproducing Kernel Spaces and Lemmas
38(2)
The Representation of Solution of TVP (2.3.6)
40(1)
Numerical Experiments
41(2)
Solving a Class of Variable Delay Integro-Differential Equations
43(10)
Introduction
43(1)
The Reproducing Kernel Spaces
44(1)
Linear Operator L on W32[ 0,)
45(3)
Two Function Sequences: rn(x), rn(x)
48(1)
The Representation of Solution of Eq. (2.4.4)
49(1)
Numerical Experiments
50(3)
Some Algebras Problems
53(22)
Solving Infinite System of Linear Equations
53(14)
Introduction
53(1)
A Norm-Preserving Operator ρ from l2onto W12[ 0, 1]
54(1)
Transform Infinite System of Linear Equation Ay = b into Operator Equation Ku = f on W12[ 0,1]
55(1)
Representation of the Solution for Infinite System of Linear Equations Ay = b
56(4)
Recursion Relation
60(2)
Numerical Experiments
62(5)
A Solution of Infinite System of Quadratic Equations
67(8)
Introduction
67(1)
Linear Operators in Reproducing Kernel Space
68(4)
Separated Solution of (3.2.10)
72(3)
II 2
75(132)
Integral equations
77(34)
Solving Fredholm Integral Equations of the First Kind and A Stability Analysis
77(8)
Introduction
77(1)
Representation of Exact Solution for Fredholm Integral Equation of the First Kind
78(3)
The Stability of the Solution on the Eq. (4.1.3)
81(1)
Numerical Experiments
82(3)
Solving Nonlinear Volterra-Fredholm Integral Equations
85(8)
Introduction
85(1)
Theoretic Basis of the Method
86(1)
Implementations of the Method
87(4)
Numerical Experiment
91(2)
Solving a Class of Nonlinear Volterra-Fredholm Integral Equations
93(7)
Introduction
93(1)
Solving Eq. (4.3.1) in the Reproducing Kernel Space
94(3)
Numerical Experiments
97(3)
New Algorithm for Nonlinear Integro-Differential Equation
100(11)
Introduction
100(1)
Solving the Nonlinear Operator Equation
100(5)
The Algorithm of Finding the Separable Solution
105(2)
Numerical Experiments
107(4)
Differential Equations
111(58)
Solving Variable-Coefficient Burgers Equation
111(11)
Introduction
111(1)
The Solution of Eq. (5.1.3)
112(2)
The Implementation Method
114(5)
Numerical Experiments
119(3)
The Nonlinear Age-Structured Population Model
122(17)
Numerical Experiments
122(1)
Solving Population Model can be Turned into Solving Operator Equation (IV)
123(8)
The Exact Solution of Eq.(IV)
131(8)
Numerical Experiments
139(1)
Solving a Kind of Nonlinear Partial Differential Equations
139(7)
Introduction
139(2)
Transformation of the Nonlinear Partial Differential Equation
141(1)
The Definition of Operator L
142(1)
Decomposition into Direct Sum of W2(2, 3)(D)
142(1)
Solving the Nonlinear Partial Differential Equation
143(2)
Numerical Experiments
145(1)
Solving the Damped Nonlinear Klein-Gordon Equation
146(9)
Introduction
146(1)
Linear Operator on Reproducing Kernel Spaces
147(2)
The Solution of Eq. (5.4.3)
149(2)
Numerical experiments
151(3)
Conclusion
154(1)
Solving a Nonlinear Second Order System
155(6)
Introduction
155(1)
Several Reproducing Kernel Spaces and Lemmas
155(2)
The Analytical and Approximate Solutions of Eq. (5.5.2)
157(3)
Numerical Experiments
160(1)
To Solve a Class of Nonlinear Differential Equations
161(8)
Introduction
161(2)
Linear Operator on Reproducing Kernel Spaces
163(1)
Direct Sum of W2(3, 1)(D)
164(1)
Solution of (Lw)(x) = f(x)
165(2)
Example
167(2)
The Exact Solution of Nonlinear Operator Equation AuBu+Cu = f
169(18)
Introduction
169(7)
Preliminary Knowledge
170(1)
Operator K
170(2)
About Eq. (6.1.10) and Eq. (6.1.6)
172(1)
Solving Eq. (6.1.10)
173(1)
Numerical Experiments
174(2)
All Solutions of System of Ill-Posed Operator Equations of the First Kind
176(11)
Introduction
176(1)
Lemmas
176(5)
Solving Au = f in Reproducing Kernel Sapce
181(2)
Numerical Experiments
183(4)
Solving the Inverse Problems
187(20)
Solving the Coefficient Inverse Problem
187(10)
Introduction
187(2)
The Reproducing Kernel Spaces
189(1)
Transformation of Eq. (7.1.1)
190(2)
Decomposition into Direct Sum of W2(3, 3)(D)
192(2)
The Method of Solving Eq. (7.1.6)
194(2)
Numerical Experiments
196(1)
A Determination of an Unknown Parameter in Parabolic Equations
197(10)
Introduction
197(2)
The Exact Solution of Eq. (7.2.4)
199(1)
An Iteration Procedure
200(3)
Numerical Experiments
203(4)
Bibliography 207(16)
Index 223