Discrete variable methods in ordinary differential equations / Peter Henrici.

Por: Henrici, Peter, 1923-Editor: New York : Wiley, c1962Descripción: xi, 407 p. : il. ; 24 cmOtra clasificación: 65.61
Contenidos:
0.1. Definitions. Classification of problems, [1]
0.2. Necessity of numerical methods for solving differential equations, [2]
0.3. Discrete variable methods, 3 Notes, [5]
PART I. ONE-STEP METHODS FOR INITIAL VALUE PROBLEMS [7]
Chapter 1. Euler’s method for a single equation of the first order, [9]
1.1. Introduction, [9]
1.2. The existence of a solution of the initial value problem, [15]
1.3. The discretization error of Euler’s method, [26]
1.4. The round-off error in Euler’s method, [35]
1.5. Random variables, [41]
1.6. Probabilistic theory of round-off errors, [50]
1.7. Problems for solution, 59 Notes, [63]
Chapter 2, General one-step methods for a single equation of the first order, [64]
2.1. Special one-step methods, [65]
2.2. The discretization error of the general one-step method, [70]
2.3. The round-off error in the general one-step method, [87]
2.4. Problems for solution, [100]
Notes, [106]
Chapter 3. General one-step methods for systems of equations of the first order, [108]
3.1. Theoretical introduction, [108]
3.2. Special one-step methods for systems, [117]
3.3. The discretization error of one-step methods, [123]
3.4. The round-off error in the integration of systems by one-step methods, [137]
3.5. Problems for solution, 158 Notes, [163]
Chapter 4. One-step methods for systems of equations of higher order, [164]
4.1. Introduction, [164]
4.2. Numerical methods for system of equations of higher order, [167]
4.3. Discretization error, [173]
4.4. Propagation of round-off error, [178]
4.5. Problems for solution, [181]
Notes, [184]
PART II. MULTISTEP METHODS FOR INITIAL VALUE PROBLEMS [185]
Chapter 5. Multistep methods for equations of the first order, [187]
5.1. Special multistep methods, [187]
5.2. General discussion of linear multistep methods, [209]
5.3. The discretization error of linear multistep methods, [235]
5.4. Round-off error in the integration by multistep methods, [262]
5.5. Problems and supplementary remarks, 281 Notes, [287]
Chapter 6. Multistep methods for special equations of the second order, [289]
6.1. Local study of linear multistep methods, [290]
6.2. The discretization error, [312]
6.3. Propagation of round-off error, [318]
6.4. Summed form of the difference equations, [327]
6.5. Problems and supplementary remarks, [339]
Notes, [342]
PART III. BOUNDARY VALUE PROBLEMS [345]
Chapter 7. Direct methods for a class of nonlinear boundary value problems of the second order, [347]
7.1. Method of solution, [347]
7.2. Existence of a solution of the difference scheme, [358]
7.3. The discretization error in boundary problems of class M, [374]
7.4. Influence of round-off error, [377]
7.5. Problems and supplementary remarks, 384 Notes, [388]
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Libros Libros Instituto de Matemática, CONICET-UNS
Libros ordenados por tema 65 H518d (Browse shelf) Available A-3139

ANÁLISIS NUMÉRICO

MÉTODOS NUMÉRICOS PARA ECUACIONES DIFERENCIALES

Libros Libros Instituto de Matemática, CONICET-UNS
Libros ordenados por tema 65 H518d (Browse shelf) Ej. 2 Available A-3695

Bibliografía: p. 389-400.

0.1. Definitions. Classification of problems, [1] --
0.2. Necessity of numerical methods for solving differential equations, [2] --
0.3. Discrete variable methods, 3 Notes, [5] --
PART I. ONE-STEP METHODS FOR INITIAL VALUE PROBLEMS [7] --
Chapter 1. Euler’s method for a single equation of the first order, [9] --
1.1. Introduction, [9] --
1.2. The existence of a solution of the initial value problem, [15] --
1.3. The discretization error of Euler’s method, [26] --
1.4. The round-off error in Euler’s method, [35] --
1.5. Random variables, [41] --
1.6. Probabilistic theory of round-off errors, [50] --
1.7. Problems for solution, 59 Notes, [63] --
Chapter 2, General one-step methods for a single equation of the first order, [64] --
2.1. Special one-step methods, [65] --
2.2. The discretization error of the general one-step method, [70] --
2.3. The round-off error in the general one-step method, [87] --
2.4. Problems for solution, [100] --
Notes, [106] --
Chapter 3. General one-step methods for systems of equations of the first order, [108] --
3.1. Theoretical introduction, [108] --
3.2. Special one-step methods for systems, [117] --
3.3. The discretization error of one-step methods, [123] --
3.4. The round-off error in the integration of systems by one-step methods, [137] --
3.5. Problems for solution, 158 Notes, [163] --
Chapter 4. One-step methods for systems of equations of higher order, [164] --
4.1. Introduction, [164] --
4.2. Numerical methods for system of equations of higher order, [167] --
4.3. Discretization error, [173] --
4.4. Propagation of round-off error, [178] --
4.5. Problems for solution, [181] --
Notes, [184] --
PART II. MULTISTEP METHODS FOR INITIAL VALUE PROBLEMS [185] --
Chapter 5. Multistep methods for equations of the first order, [187] --
5.1. Special multistep methods, [187] --
5.2. General discussion of linear multistep methods, [209] --
5.3. The discretization error of linear multistep methods, [235] --
5.4. Round-off error in the integration by multistep methods, [262] --
5.5. Problems and supplementary remarks, 281 Notes, [287] --
Chapter 6. Multistep methods for special equations of the second order, [289] --
6.1. Local study of linear multistep methods, [290] --
6.2. The discretization error, [312] --
6.3. Propagation of round-off error, [318] --
6.4. Summed form of the difference equations, [327] --
6.5. Problems and supplementary remarks, [339] --
Notes, [342] --
PART III. BOUNDARY VALUE PROBLEMS [345] --
Chapter 7. Direct methods for a class of nonlinear boundary value problems of the second order, [347] --
7.1. Method of solution, [347] --
7.2. Existence of a solution of the difference scheme, [358] --
7.3. The discretization error in boundary problems of class M, [374] --
7.4. Influence of round-off error, [377] --
7.5. Problems and supplementary remarks, 384 Notes, [388] --

MR, 24 #B1772

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