Muutke küpsiste eelistusi

Numerical Methods for Two-Point Boundary-Value Problems [Pehme köide]

5.00/5 (1 hinnangut Goodreads-ist)
  • Formaat: Paperback / softback, 416 pages, kõrgus x laius x paksus: 215x140x21 mm, kaal: 500 g
  • Ilmumisaeg: 28-Dec-2018
  • Kirjastus: Dover Publications Inc.
  • ISBN-10: 0486828344
  • ISBN-13: 9780486828343
Teised raamatud teemal:
  • Pehme köide
  • Hind: 37,20 €*
  • * saadame teile pakkumise kasutatud raamatule, mille hind võib erineda kodulehel olevast hinnast
  • See raamat on trükist otsas, kuid me saadame teile pakkumise kasutatud raamatule.
  • Kogus:
  • Lisa ostukorvi
  • Tasuta tarne
  • Lisa soovinimekirja
Numerical Methods for Two-Point Boundary-Value ProblemsSuurem pilt
  • Formaat: Paperback / softback, 416 pages, kõrgus x laius x paksus: 215x140x21 mm, kaal: 500 g
  • Ilmumisaeg: 28-Dec-2018
  • Kirjastus: Dover Publications Inc.
  • ISBN-10: 0486828344
  • ISBN-13: 9780486828343
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780486828343.html
Märksõnad:
Elementary yet rigorous, this concise treatment explores practical numerical methods for solving very general two-point boundary-value problems. The approach is directed toward students with a knowledge of advanced calculus and basic numerical analysis as well as some background in ordinary differential equations and linear algebra.
After an introductory chapter that covers some of the basic prerequisites, the text studies three techniques in detail: initial value or "shooting" methods, finite difference methods, and integral equations methods. Sturm-Liouville eigenvalue problems are treated with all three techniques, and shooting is applied to generalized or nonlinear eigenvalue problems. Several other areas of numerical analysis are introduced throughout the study. The treatment concludes with more than 100 problems that augment and clarify the text, and several research papers appear in the Appendixes.


Elementary yet rigorous, this concise treatment is directed toward students with a knowledge of advanced calculus, basic numerical analysis, and some background in ordinary differential equations and linear algebra. 1968 edition.
Chapter 1 Introduction
1(38)
1.1 Initial-Value Problems
1(6)
1.2 Two-Point Boundary-Value Problems
7(14)
1.2.1 Boundary-Value Problems for General Systems
13(8)
1.3 Numerical Methods for Initial-Value Problems
21(9)
1.4 Iterative Solution of Nonlinear Systems; Contracting Maps
30(9)
Chapter 2 Initial-Value Methods (Shooting)
39(33)
2.1 Linear Second-Order Equations and Systems
39(8)
2.2 Nonlinear Second-Order Equations
47(7)
2.3 Linear and Nonlinear Systems
54(7)
2.4 Variants of Shooting; Parallel Shooting
61(11)
2.4.1 Power Series
68(4)
Chapter 3 Finite-Difference Methods
72(34)
3.1 Linear Second-Order Equations
72(11)
3.1.1 Difference Corrections and h → 0 Extrapolation
78(5)
3.2 Nonlinear Second-Order Equations
83(8)
3.3 Linear and Nonlinear Systems
91(15)
3.3.1 Difference Corrections and h → 0 Extrapolation
100(6)
Chapter 4 Integral-Equation Methods
106(16)
4.1 Green's Functions; Equivalent Integral Equations
106(6)
4.2 Numerical Solution of Integral Equations
112(10)
Chapter 5 Eigenvalue Problems
122(31)
5.1 Introduction; Sturm-Liouville Problems
122(3)
5.2 Initial-Value Methods for Eigenvalue Problems
125(6)
5.3 Finite-Difference Methods
131(7)
5.4 Eigenvalue Problems for Integral Equations
138(4)
5.5 Generalized Eigenvalue Problems
142(11)
5.5.1 Poineare Continuation, Continuity Methods
146(7)
Chapter 6 Practical Examples and Computational Exercises
153(20)
Introduction
153(1)
6.1 Shooting; Lubrication Theory
153(9)
6.1.1 Computing Exercise; Forced Flow
160(2)
6.2 Finite Differences; Biophysics
162(11)
6.2.1 H → 0 Extrapolation
168(2)
6.2.2 Computing Exercise; Nonlinear Diffusivity
170(3)
APPENDIX A FUNCTION SPACE APPROXIMATION METHODS
173(12)
1 Galerkin's Method
173(2)
2 Collocation Methods
175(1)
3 Generalized Ritz Methods
176(2)
Bibliography
178(5)
Index
183(2)
APPENDIX B NUMERICAL SOLUTION OF TWO-POINT BOUNDARY-VALUE PROBLEMS
185(68)
1 Shooting Methods
191(20)
2 Finite Difference Methods
211(18)
3 Eigenvalue Problems
229(10)
4 Singular Problems
239(14)
APPENDIX C SOME FURTHER RESULTS
253
1 Newton's Method under Mild Differentiability Conditions
255(14)
2 Approximation Methods for Nonlinear Problems with Application to Two-Point Boundary-Value Problems
269(12)
3 Accurate Difference Methods for Linear Ordinary Differential Systems Subject to Linear Constraints
281(24)
4 Accurate Difference Methods for Nonlinear Two-Point Boundary-Value Problems
305(16)
5 Difference Methods for Boundary-Value Problems in Ordinary Differential Equations
321(12)
6 A Numerical Method for Singular Two-Point Boundary-Value Problems
333(14)
7 Numerical Solution of Bifurcation and Nonlinear Eigenvalue Problems
347(26)
8 Shooting and Parallel Shooting Methods for Solving the Falkner-Skan Boundary-Layer Equation
373(12)
9 The Von Karman Swirling Flows
385