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I-Smooth analysis : theory and applications / / A. V. Kim
| I-Smooth analysis : theory and applications / / A. V. Kim |
| Autore | Kim A. V. |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Salem, Massachusetts : , : Scrivener Publishing, , 2015 |
| Descrizione fisica | 1 online resource (294 p.) |
| Disciplina | 515 |
| Soggetto topico |
Functional differential equations - Numerical solutions
Functional analysis - Research |
| ISBN |
1-118-99854-5
1-118-99851-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Copyright Page; Contents; Preface; Part I Invariant derivatives of functionals and numerical methods for functional differential equations; 1 The invariant derivative of functionals; 1 Functional derivatives; 1.1 The Frechet derivative; 1.2 The Gateaux derivative; 2 Classifi cation of functionals on C[a, b]; 2.1 Regular functionals; 2.2 Singular functionals; 3 Calculation of a functional along a line; 3.1 Shift operators; 3.2 Superposition of a functional and a function; 3.3 Dini derivatives; 4 Discussion of two examples; 4.1 Derivative of a function along a curve
4.2 Derivative of a functional along a curve5 The invariant derivative; 5.1 The invariant derivative; 5.2 The invariant derivative in the class B[a, b]; 5.3 Examples; 6 Properties of the invariant derivative; 6.1 Principles of calculating invariant derivatives; 6.2 The invariant differentiability and invariant continuity; 6.3 High order invariant derivatives; 6.4 Series expansion; 7 Several variables; 7.1 Notation; 7.2 Shift operator; 7.3 Partial invariant derivative; 8 Generalized derivatives of nonlinear functionals; 8.1 Introduction; 8.2 Distributions (generalized functions) 13.1 Functional Differential Equations13.2 FDE types; 13.3 Modeling by FDE; 13.4 Phase space and FDE conditional representation; 14 Existence and uniqueness of FDE solutions; 14.1 The classic solutions; 14.2 Caratheodory solutions; 14.3 The step method for systems with discrete delays; 15 Smoothness of solutions and expansion into the Taylor series; 15.1 Density of special initial functions; 15.2 Expansion of FDE solutions into Taylor series; 16 The sewing procedure; 16.1 General case; 16.2 Sewing (modification) by polynomials; 16.3 The sewing procedure of the second order 16.4 Sewing procedure of the second order for linear delay differential equation |
| Record Nr. | UNINA-9910140640203321 |
Kim A. V.
|
||
| Salem, Massachusetts : , : Scrivener Publishing, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
I-Smooth analysis : theory and applications / / A. V. Kim
| I-Smooth analysis : theory and applications / / A. V. Kim |
| Autore | Kim A. V. |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Salem, Massachusetts : , : Scrivener Publishing, , 2015 |
| Descrizione fisica | 1 online resource (294 p.) |
| Disciplina | 515 |
| Soggetto topico |
Functional differential equations - Numerical solutions
Functional analysis - Research |
| ISBN |
1-118-99854-5
1-118-99851-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Copyright Page; Contents; Preface; Part I Invariant derivatives of functionals and numerical methods for functional differential equations; 1 The invariant derivative of functionals; 1 Functional derivatives; 1.1 The Frechet derivative; 1.2 The Gateaux derivative; 2 Classifi cation of functionals on C[a, b]; 2.1 Regular functionals; 2.2 Singular functionals; 3 Calculation of a functional along a line; 3.1 Shift operators; 3.2 Superposition of a functional and a function; 3.3 Dini derivatives; 4 Discussion of two examples; 4.1 Derivative of a function along a curve
4.2 Derivative of a functional along a curve5 The invariant derivative; 5.1 The invariant derivative; 5.2 The invariant derivative in the class B[a, b]; 5.3 Examples; 6 Properties of the invariant derivative; 6.1 Principles of calculating invariant derivatives; 6.2 The invariant differentiability and invariant continuity; 6.3 High order invariant derivatives; 6.4 Series expansion; 7 Several variables; 7.1 Notation; 7.2 Shift operator; 7.3 Partial invariant derivative; 8 Generalized derivatives of nonlinear functionals; 8.1 Introduction; 8.2 Distributions (generalized functions) 13.1 Functional Differential Equations13.2 FDE types; 13.3 Modeling by FDE; 13.4 Phase space and FDE conditional representation; 14 Existence and uniqueness of FDE solutions; 14.1 The classic solutions; 14.2 Caratheodory solutions; 14.3 The step method for systems with discrete delays; 15 Smoothness of solutions and expansion into the Taylor series; 15.1 Density of special initial functions; 15.2 Expansion of FDE solutions into Taylor series; 16 The sewing procedure; 16.1 General case; 16.2 Sewing (modification) by polynomials; 16.3 The sewing procedure of the second order 16.4 Sewing procedure of the second order for linear delay differential equation |
| Record Nr. | UNISA-996216082203316 |
|
Kim A. V.
|
||
| Salem, Massachusetts : , : Scrivener Publishing, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
I-Smooth analysis : theory and applications / / A. V. Kim
| I-Smooth analysis : theory and applications / / A. V. Kim |
| Autore | Kim A. V. |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Salem, Massachusetts : , : Scrivener Publishing, , 2015 |
| Descrizione fisica | 1 online resource (294 p.) |
| Disciplina | 515 |
| Soggetto topico |
Functional differential equations - Numerical solutions
Functional analysis - Research |
| ISBN |
1-118-99854-5
1-118-99851-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Copyright Page; Contents; Preface; Part I Invariant derivatives of functionals and numerical methods for functional differential equations; 1 The invariant derivative of functionals; 1 Functional derivatives; 1.1 The Frechet derivative; 1.2 The Gateaux derivative; 2 Classifi cation of functionals on C[a, b]; 2.1 Regular functionals; 2.2 Singular functionals; 3 Calculation of a functional along a line; 3.1 Shift operators; 3.2 Superposition of a functional and a function; 3.3 Dini derivatives; 4 Discussion of two examples; 4.1 Derivative of a function along a curve
4.2 Derivative of a functional along a curve5 The invariant derivative; 5.1 The invariant derivative; 5.2 The invariant derivative in the class B[a, b]; 5.3 Examples; 6 Properties of the invariant derivative; 6.1 Principles of calculating invariant derivatives; 6.2 The invariant differentiability and invariant continuity; 6.3 High order invariant derivatives; 6.4 Series expansion; 7 Several variables; 7.1 Notation; 7.2 Shift operator; 7.3 Partial invariant derivative; 8 Generalized derivatives of nonlinear functionals; 8.1 Introduction; 8.2 Distributions (generalized functions) 13.1 Functional Differential Equations13.2 FDE types; 13.3 Modeling by FDE; 13.4 Phase space and FDE conditional representation; 14 Existence and uniqueness of FDE solutions; 14.1 The classic solutions; 14.2 Caratheodory solutions; 14.3 The step method for systems with discrete delays; 15 Smoothness of solutions and expansion into the Taylor series; 15.1 Density of special initial functions; 15.2 Expansion of FDE solutions into Taylor series; 16 The sewing procedure; 16.1 General case; 16.2 Sewing (modification) by polynomials; 16.3 The sewing procedure of the second order 16.4 Sewing procedure of the second order for linear delay differential equation |
| Record Nr. | UNINA-9910830294703321 |
|
Kim A. V.
|
||
| Salem, Massachusetts : , : Scrivener Publishing, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Systems with delays : analysis, control, and computations / / A. V. Kim and A. V. Ivanov
| Systems with delays : analysis, control, and computations / / A. V. Kim and A. V. Ivanov |
| Autore | Kim A. V. |
| Pubbl/distr/stampa | Hoboken, New Jersey ; ; Salem, Massachusetts : , : Scrivener Publishing : , : Wiley, , 2015 |
| Descrizione fisica | 1 online resource (180 p.) |
| Disciplina | 515/.35 |
| Soggetto topico |
Delay differential equations
Linear systems Derivatives (Mathematics) |
| ISBN |
1-119-11773-9
1-119-11784-4 1-119-11772-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
2.2 Lyapunov-Krasovskii functionals2.2.1 Structure of Lyapunov-Krasovskii quadratic functionals; 2.2.2 Elementary functionals and their properties; 2.2.3 Total derivative of functionals with respect to systems with delays; 2.3 Positiveness of functionals; 2.3.1 Definitions; 2.3.2 Sufficient conditions of positiveness; 2.3.3 Positiveness of functionals; 2.4 Stability via Lyapunov-Krasovskii functionals; 2.4.1 Stability conditions in the norm || · || H; 2.4.2 Stability conditions in the norm || · ||; 2.4.3 Converse theorem; 2.4.4 Examples; 2.5 Coefficient conditions of stability
2.5.1 Linear system with discrete delay2.5.2 Linear system with distributed delays; 3 Linear quadratic control; 3.1 Introduction; 3.2 Statement of the problem; 3.3 Explicit solutions of generalized Riccati equations; 3.3.1 Variant 1; 3.3.2 Variant 2; 3.3.3 Variant 3; 3.4 Solution of Exponential Matrix Equation; 3.4.1 Stationary solution method; 3.4.2 Gradient methods; 3.5 Design procedure; 3.5.1 Variants 1 and 2; 3.5.2 Variant 3; 3.6 Design case studies; 3.6.1 Example 1; 3.6.2 Example 2; 3.6.3 Example 3; 3.6.4 Example 4; 3.6.5 Example 5: Wind tunnel model 3.6.6 Example 6: Combustion stability in liquid propellant rocket motors4 Numerical methods; 4.1 Introduction; 4.2 Elementary one-step methods; 4.2.1 Euler'smethod; 4.2.2 Implicit methods (extrapolation); 4.2.3 Improved Euler'smethod; 4.2.4 Runge-Kutta-like methods; 4.3 Interpolation and extrapolation of the model pre-history; 4.3.1 Interpolational operators; 4.3.2 Extrapolational operators; 4.3.3 Interpolation-Extrapolation operator; 4.4 Explicit Runge-Kutta-like methods; 4.5 Approximation orders of ERK-like methods; 4.6 Automatic step size control; 4.6.1 Richardson extrapolation 4.6.2 Automatic step size control |
| Record Nr. | UNINA-9910131493003321 |
|
Kim A. V.
|
||
| Hoboken, New Jersey ; ; Salem, Massachusetts : , : Scrivener Publishing : , : Wiley, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Systems with delays : analysis, control, and computations / / A. V. Kim and A. V. Ivanov
| Systems with delays : analysis, control, and computations / / A. V. Kim and A. V. Ivanov |
| Autore | Kim A. V. |
| Pubbl/distr/stampa | Hoboken, New Jersey ; ; Salem, Massachusetts : , : Scrivener Publishing : , : Wiley, , 2015 |
| Descrizione fisica | 1 online resource (180 p.) |
| Disciplina | 515/.35 |
| Soggetto topico |
Delay differential equations
Linear systems Derivatives (Mathematics) |
| ISBN |
1-119-11773-9
1-119-11784-4 1-119-11772-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
2.2 Lyapunov-Krasovskii functionals2.2.1 Structure of Lyapunov-Krasovskii quadratic functionals; 2.2.2 Elementary functionals and their properties; 2.2.3 Total derivative of functionals with respect to systems with delays; 2.3 Positiveness of functionals; 2.3.1 Definitions; 2.3.2 Sufficient conditions of positiveness; 2.3.3 Positiveness of functionals; 2.4 Stability via Lyapunov-Krasovskii functionals; 2.4.1 Stability conditions in the norm || · || H; 2.4.2 Stability conditions in the norm || · ||; 2.4.3 Converse theorem; 2.4.4 Examples; 2.5 Coefficient conditions of stability
2.5.1 Linear system with discrete delay2.5.2 Linear system with distributed delays; 3 Linear quadratic control; 3.1 Introduction; 3.2 Statement of the problem; 3.3 Explicit solutions of generalized Riccati equations; 3.3.1 Variant 1; 3.3.2 Variant 2; 3.3.3 Variant 3; 3.4 Solution of Exponential Matrix Equation; 3.4.1 Stationary solution method; 3.4.2 Gradient methods; 3.5 Design procedure; 3.5.1 Variants 1 and 2; 3.5.2 Variant 3; 3.6 Design case studies; 3.6.1 Example 1; 3.6.2 Example 2; 3.6.3 Example 3; 3.6.4 Example 4; 3.6.5 Example 5: Wind tunnel model 3.6.6 Example 6: Combustion stability in liquid propellant rocket motors4 Numerical methods; 4.1 Introduction; 4.2 Elementary one-step methods; 4.2.1 Euler'smethod; 4.2.2 Implicit methods (extrapolation); 4.2.3 Improved Euler'smethod; 4.2.4 Runge-Kutta-like methods; 4.3 Interpolation and extrapolation of the model pre-history; 4.3.1 Interpolational operators; 4.3.2 Extrapolational operators; 4.3.3 Interpolation-Extrapolation operator; 4.4 Explicit Runge-Kutta-like methods; 4.5 Approximation orders of ERK-like methods; 4.6 Automatic step size control; 4.6.1 Richardson extrapolation 4.6.2 Automatic step size control |
| Record Nr. | UNINA-9910812670503321 |
|
Kim A. V.
|
||
| Hoboken, New Jersey ; ; Salem, Massachusetts : , : Scrivener Publishing : , : Wiley, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||