Discrete variable methods in ordinary differential equations / Peter Henrici.
Editor: New York : Wiley, c1962Descripción: xi, 407 p. : il. ; 24 cmOtra clasificación: 65.610.1. 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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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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