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Numerical solution of ordinary differential equations / / Kendall E. Atkinson, Weimin Han, David Stewart
| Numerical solution of ordinary differential equations / / Kendall E. Atkinson, Weimin Han, David Stewart |
| Autore | Atkinson Kendall E. |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2009 |
| Descrizione fisica | 1 online resource (272 p.) |
| Disciplina | 515.352 |
| Collana | Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs, and Tracts |
| Soggetto topico | Differential equations - Numerical solutions |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-33249-3
9786613332493 1-118-16449-0 1-118-16452-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Numerical Solution of Ordinary Differential Equations; CONTENTS; Introduction; 1 Theory of differential equations: An introduction; 1.1 General solvability theory; 1.2 Stability of the initial value problem; 1.3 Direction fields; Problems; 2 Euler's method; 2.1 Definition of Euler's method; 2.2 Error analysis of Euler's method; 2.3 Asymptotic error analysis; 2.3.1 Richardson extrapolation; 2.4 Numerical stability; 2.4.1 Rounding error accumulation; Problems; 3 Systems of differential equations; 3.1 Higher-order differential equations; 3.2 Numerical methods for systems; Problems
4 The backward Euler method and the trapezoidal method4.1 The backward Euler method; 4.2 The trapezoidal method; Problems; 5 Taylor and Runge-Kutta methods; 5.1 Taylor methods; 5.2 Runge-Kutta methods; 5.2.1 A general framework for explicit Runge-Kutta methods; 5.3 Convergence, stability, and asymptotic error; 5.3.1 Error prediction and control; 5.4 Runge-Kutta-Fehlberg methods; 5.5 MATLAB codes; 5.6 Implicit Runge-Kutta methods; 5.6.1 Two-point collocation methods; Problems; 6 Multistep methods; 6.1 Adams-Bashforth methods; 6.2 Adams-Moulton methods; 6.3 Computer codes 6.3.1 MATLAB ODE codesProblems; 7 General error analysis for multistep methods; 7.1 Truncation error; 7.2 Convergence; 7.3 A general error analysis; 7.3.1 Stability theory; 7.3.2 Convergence theory; 7.3.3 Relative stability and weak stability; Problems; 8 Stiff differential equations; 8.1 The method of lines for a parabolic equation; 8.1.1 MATLAB programs for the method of lines; 8.2 Backward differentiation formulas; 8.3 Stability regions for multistep methods; 8.4 Additional sources of difficulty; 8.4.1 A-stability and L-stability; 8.4.2 Time-varying problems and stability 8.5 Solving the finite-difference method8.6 Computer codes; Problems; 9 Implicit RK methods for stiff differential equations; 9.1 Families of implicit Runge-Kutta methods; 9.2 Stability of Runge-Kutta methods; 9.3 Order reduction; 9.4 Runge-Kutta methods for stiff equations in practice; Problems; 10 Differential algebraic equations; 10.1 Initial conditions and drift; 10.2 DAEs as stiff differential equations; 10.3 Numerical issues: higher index problems; 10.4 Backward differentiation methods for DAEs; 10.4.1 Index 1 problems; 10.4.2 Index 2 problems; 10.5 Runge-Kutta methods for DAEs 10.5.1 Index 1 problems10.5.2 Index 2 problems; 10.6 Index three problems from mechanics; 10.6.1 Runge-Kutta methods for mechanical index 3 systems; 10.7 Higher index DAEs; Problems; 11 Two-point boundary value problems; 11.1 A finite-difference method; 11.1.1 Convergence; 11.1.2 A numerical example; 11.1.3 Boundary conditions involving the derivative; 11.2 Nonlinear two-point boundary value problems; 11.2.1 Finite difference methods; 11.2.2 Shooting methods; 11.2.3 Collocation methods; 11.2.4 Other methods and problems; Problems; 12 Volterra integral equations; 12.1 Solvability theory 12.1.1 Special equations |
| Record Nr. | UNISA-996213326003316 |
Atkinson Kendall E.
|
||
| Hoboken, New Jersey : , : Wiley, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Numerical solution of ordinary differential equations / / Kendall E. Atkinson, Weimin Han, David Stewart
| Numerical solution of ordinary differential equations / / Kendall E. Atkinson, Weimin Han, David Stewart |
| Autore | Atkinson Kendall E. |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2009 |
| Descrizione fisica | 1 online resource (272 p.) |
| Disciplina | 515.352 |
| Collana | Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs, and Tracts |
| Soggetto topico | Differential equations - Numerical solutions |
| ISBN |
1-283-33249-3
9786613332493 1-118-16449-0 1-118-16452-0 |
| Classificazione | SK 920 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Numerical Solution of Ordinary Differential Equations; CONTENTS; Introduction; 1 Theory of differential equations: An introduction; 1.1 General solvability theory; 1.2 Stability of the initial value problem; 1.3 Direction fields; Problems; 2 Euler's method; 2.1 Definition of Euler's method; 2.2 Error analysis of Euler's method; 2.3 Asymptotic error analysis; 2.3.1 Richardson extrapolation; 2.4 Numerical stability; 2.4.1 Rounding error accumulation; Problems; 3 Systems of differential equations; 3.1 Higher-order differential equations; 3.2 Numerical methods for systems; Problems
4 The backward Euler method and the trapezoidal method4.1 The backward Euler method; 4.2 The trapezoidal method; Problems; 5 Taylor and Runge-Kutta methods; 5.1 Taylor methods; 5.2 Runge-Kutta methods; 5.2.1 A general framework for explicit Runge-Kutta methods; 5.3 Convergence, stability, and asymptotic error; 5.3.1 Error prediction and control; 5.4 Runge-Kutta-Fehlberg methods; 5.5 MATLAB codes; 5.6 Implicit Runge-Kutta methods; 5.6.1 Two-point collocation methods; Problems; 6 Multistep methods; 6.1 Adams-Bashforth methods; 6.2 Adams-Moulton methods; 6.3 Computer codes 6.3.1 MATLAB ODE codesProblems; 7 General error analysis for multistep methods; 7.1 Truncation error; 7.2 Convergence; 7.3 A general error analysis; 7.3.1 Stability theory; 7.3.2 Convergence theory; 7.3.3 Relative stability and weak stability; Problems; 8 Stiff differential equations; 8.1 The method of lines for a parabolic equation; 8.1.1 MATLAB programs for the method of lines; 8.2 Backward differentiation formulas; 8.3 Stability regions for multistep methods; 8.4 Additional sources of difficulty; 8.4.1 A-stability and L-stability; 8.4.2 Time-varying problems and stability 8.5 Solving the finite-difference method8.6 Computer codes; Problems; 9 Implicit RK methods for stiff differential equations; 9.1 Families of implicit Runge-Kutta methods; 9.2 Stability of Runge-Kutta methods; 9.3 Order reduction; 9.4 Runge-Kutta methods for stiff equations in practice; Problems; 10 Differential algebraic equations; 10.1 Initial conditions and drift; 10.2 DAEs as stiff differential equations; 10.3 Numerical issues: higher index problems; 10.4 Backward differentiation methods for DAEs; 10.4.1 Index 1 problems; 10.4.2 Index 2 problems; 10.5 Runge-Kutta methods for DAEs 10.5.1 Index 1 problems10.5.2 Index 2 problems; 10.6 Index three problems from mechanics; 10.6.1 Runge-Kutta methods for mechanical index 3 systems; 10.7 Higher index DAEs; Problems; 11 Two-point boundary value problems; 11.1 A finite-difference method; 11.1.1 Convergence; 11.1.2 A numerical example; 11.1.3 Boundary conditions involving the derivative; 11.2 Nonlinear two-point boundary value problems; 11.2.1 Finite difference methods; 11.2.2 Shooting methods; 11.2.3 Collocation methods; 11.2.4 Other methods and problems; Problems; 12 Volterra integral equations; 12.1 Solvability theory 12.1.1 Special equations |
| Record Nr. | UNINA-9910141193403321 |
|
Atkinson Kendall E.
|
||
| Hoboken, New Jersey : , : Wiley, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Numerical solution of ordinary differential equations / / Kendall E. Atkinson, Weimin Han, David Stewart
| Numerical solution of ordinary differential equations / / Kendall E. Atkinson, Weimin Han, David Stewart |
| Autore | Atkinson Kendall E. |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2009 |
| Descrizione fisica | 1 online resource (272 p.) |
| Disciplina | 515.352 |
| Collana | Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs, and Tracts |
| Soggetto topico | Differential equations - Numerical solutions |
| ISBN |
1-283-33249-3
9786613332493 1-118-16449-0 1-118-16452-0 |
| Classificazione | SK 920 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Numerical Solution of Ordinary Differential Equations; CONTENTS; Introduction; 1 Theory of differential equations: An introduction; 1.1 General solvability theory; 1.2 Stability of the initial value problem; 1.3 Direction fields; Problems; 2 Euler's method; 2.1 Definition of Euler's method; 2.2 Error analysis of Euler's method; 2.3 Asymptotic error analysis; 2.3.1 Richardson extrapolation; 2.4 Numerical stability; 2.4.1 Rounding error accumulation; Problems; 3 Systems of differential equations; 3.1 Higher-order differential equations; 3.2 Numerical methods for systems; Problems
4 The backward Euler method and the trapezoidal method4.1 The backward Euler method; 4.2 The trapezoidal method; Problems; 5 Taylor and Runge-Kutta methods; 5.1 Taylor methods; 5.2 Runge-Kutta methods; 5.2.1 A general framework for explicit Runge-Kutta methods; 5.3 Convergence, stability, and asymptotic error; 5.3.1 Error prediction and control; 5.4 Runge-Kutta-Fehlberg methods; 5.5 MATLAB codes; 5.6 Implicit Runge-Kutta methods; 5.6.1 Two-point collocation methods; Problems; 6 Multistep methods; 6.1 Adams-Bashforth methods; 6.2 Adams-Moulton methods; 6.3 Computer codes 6.3.1 MATLAB ODE codesProblems; 7 General error analysis for multistep methods; 7.1 Truncation error; 7.2 Convergence; 7.3 A general error analysis; 7.3.1 Stability theory; 7.3.2 Convergence theory; 7.3.3 Relative stability and weak stability; Problems; 8 Stiff differential equations; 8.1 The method of lines for a parabolic equation; 8.1.1 MATLAB programs for the method of lines; 8.2 Backward differentiation formulas; 8.3 Stability regions for multistep methods; 8.4 Additional sources of difficulty; 8.4.1 A-stability and L-stability; 8.4.2 Time-varying problems and stability 8.5 Solving the finite-difference method8.6 Computer codes; Problems; 9 Implicit RK methods for stiff differential equations; 9.1 Families of implicit Runge-Kutta methods; 9.2 Stability of Runge-Kutta methods; 9.3 Order reduction; 9.4 Runge-Kutta methods for stiff equations in practice; Problems; 10 Differential algebraic equations; 10.1 Initial conditions and drift; 10.2 DAEs as stiff differential equations; 10.3 Numerical issues: higher index problems; 10.4 Backward differentiation methods for DAEs; 10.4.1 Index 1 problems; 10.4.2 Index 2 problems; 10.5 Runge-Kutta methods for DAEs 10.5.1 Index 1 problems10.5.2 Index 2 problems; 10.6 Index three problems from mechanics; 10.6.1 Runge-Kutta methods for mechanical index 3 systems; 10.7 Higher index DAEs; Problems; 11 Two-point boundary value problems; 11.1 A finite-difference method; 11.1.1 Convergence; 11.1.2 A numerical example; 11.1.3 Boundary conditions involving the derivative; 11.2 Nonlinear two-point boundary value problems; 11.2.1 Finite difference methods; 11.2.2 Shooting methods; 11.2.3 Collocation methods; 11.2.4 Other methods and problems; Problems; 12 Volterra integral equations; 12.1 Solvability theory 12.1.1 Special equations |
| Record Nr. | UNINA-9910678196103321 |
|
Atkinson Kendall E.
|
||
| Hoboken, New Jersey : , : Wiley, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||