Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Linz P. — Analytical and numerical methods for Volterra equations
Linz P. — Analytical and numerical methods for Volterra equations

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Analytical and numerical methods for Volterra equations

Автор: Linz P.

Аннотация:

Presents an aspect of activity in integral equations methods for the solution of Volterra equations for those who need to solve real-world problems. Since there are few known analytical methods leading to closed-form solutions, the emphasis is on numerical techniques. The major points of the analytical methods used to study the properties of the solution are presented in the first part of the book. These techniques are important for gaining insight into the qualitative behavior of the solutions and for designing effective numerical methods. The second part of the book is devoted entirely to numerical methods.

The author has chosen the simplest possible setting for the discussion, the space of real functions of real variables. The text is supplemented by examples and exercises.



Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1985

Количество страниц: 242

Добавлена в каталог: 18.11.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$A$-stability      111
$B$-splines      209
Abel’s equation, generalized      5
Abel’s equation, inversion formulas      74
Abel’s equation, numerical solution      165
Abel’s equation, simple      4
Accumulated error, consistency      104
Accumulated error, starting      104
Adams — Moulton methods      182
Aitken’s method      134
Asymptotic behavior of solutions      42 61 89
Beltyukov methods      122
Block-by-block methods, for Abel’s equation      169
Block-by-block methods, for equations of the first kind      154
Block-by-block methods, for equations of the second kind      114
Block-by-block methods, for integrodifferential equations      185
Block-by-block methods, using product integration      136
Causality      17
Characteristic polynomial of stability      112
Comparison theorems      40 47 58
Consistency condition, for integral equations      101
Consistency condition, for integrodifferential equations      183
Consistency error, accumulated      104
Consistency error, local      101
Consistency error, order      101
Contraction mapping argument      32
Convergence, and stability      185
Convergence, of an approximation method      100
Convergence, order of      101
Conversion, differential equation to integral equation      13
Conversion, first kind equation to second kind      67 68
Conversion, integral equation into differential equation      7 78
Conversion, integrodifferential equation to integral Equation      5
Convolution equation, linear      18 77
Convolution equation, nonlinear      77
Convolution theorem      84
Dahlquist theory      177
Degenerate kernel approximation methods      126
Delay differential equation      189
Difference kernel      37
Differential resolvent      83
Differentiation methods for first kind equations      158
Direct methods for equations of the first kind      143
Discretization error      100
Effect of data errors, on Abel’s equation      204
Effect of data errors, on equations of the first kind      204
Elongation of a filament      204
Error estimates      103
Error expansion      105 121
Euler’s method      133 144
Existence of a solution, Abel’s equation      73 75
Existence of a solution, equations with unbounded kernels      48
Existence of a solution, integrodifferential equations      49
Existence of a solution, linear first kind equations      67
Existence of a solution, linear second kind equations      29
Existence of a solution, nonlinear first kind equations      69
Existence of a solution, nonlinear second kind equations      52 55
Existence of a solution, systems of the second kind      48
Finite rank kernel      8
First kind equations, nonlinear      69 160
First kind equations, numerical solution      143
First kind equations, with smooth kernels      67
Fourier transform      19
Functional equations      188
Gregory methods, for equations of the first kind      151
Gregory methods, for equations of the second kind      98
Heard method      29
Heat conduction equation      19
ill-posed problems      162
Initial value problems and Volterra equations      7
Instability in numerical computation      103
Integral equations, of Fredholm type      3
Integral equations, of Volterra type      3
Integral equations, singular      3
Integral equations, weakly singular      3
Integrodifferential equations, numerical methods      177
Integrodifferential equations, reduction to integral Equations      5
Interchanging order of integration      6
Inversion formulas, for Fourier transforms      19
Inversion formulas, for Laplace transform      84
Iterated kernels      36
Kernel, degenerate      8
Kernel, finite rank      8
Kernel, Lipschitz continuous      51
Kernel, monotonicity properties      58
Kernel, of an integral equation      4
Kernel, unbounded      4
Laplace transforms      84
Linear multistep methods      182
Lipschitz condition, for equations of the first kind      69
Lipschitz condition, for equations of the second kind      52
Lipschitz condition, for integrodifferential equations      177
Method of continuation      32
Method of successive approximation      29
Midpoint method, for Abel’s equation      166
Midpoint method, for equations of the first kind      144
Milne — Simpson methods      182
Newton — Cotes methods, for first kind equations      152
Newton — Cotes methods, for second kind equations      98
Numerical stability, equations of the first kind      149
Numerical stability, equations of the second kind      108 110
Numerical stability, integrodifferential equations      186
Pascal program, midpoint method for first kind equations      197
Pascal program, product midpoint method for first kind Equations      198
Pascal program, product trapezoidal method for second kind Equations      196
Pascal program, trapezoidal method for second kind Equations      195
Perturbation, effect, on first kind equations      71 162
Perturbation, effect, on second kind equations      45
Piecewise polynomial approximations      118 157
Polymer rheology example      204
Population equation      15
Pouzet methods      122
Predictor-corrector methods      125
Product integration      130
Product trapezoidal method, equations of the first kind      168
Product trapezoidal method, equations of the second kind      135
Radiating source      23
Reactor dynamics equation      21
Renewal, density      14
Renewal, equation      14
Repetition factor      106
Resolvent equation, difference kernels      38
Resolvent equation, linear problems      36
Resolvent equation, nonlinear problems      63
Resolvent kernel      35
Richardson’s extrapolation      133
Roundoff error, in first kind equations      161
Roundoff error, in second kind equations      121
Runge — Kutta methods, explicit      122
Runge — Kutta methods, implicit      114
Runge — Kutta methods, of Beltyukov type      122
Runge — Kutta methods, of Pouzet type      122
Second kind equations, linear      29
Second kind equations, nonlinear      51
Second kind equations, numerical solution      95
Second kind equations, product integration methods      129
Semicirculant matrix      172
Simpson’s methods      99
Stability, definition      104 183
Stability, interval      111
Starting error      104
Starting values      98
Stereology example      24
System identification      18
Systems of integral equations      5 46
Systems theory      15
Systems, causal      17
Systems, evolutionary      3
Systems, feedback      18
Systems, history-dependent      13
Systems, linear      16
Systems, nonlinear      16
Systems, time-invariant      17
Systems, with memory      13
Tauberian theorems      91
Trapezoidal method, Abel’s equation      166
Trapezoidal method, equations of the first kind      144
Trapezoidal method, integrodifferential equations      178
Uniqueness of a solution, Abel’s equation      73 75
Uniqueness of a solution, equations with an unbounded Kernel      48 62
Uniqueness of a solution, integrodifferential equation      49
Uniqueness of a solution, linear first kind equation      67
Uniqueness of a solution, linear second kind equation      29
Uniqueness of a solution, nonlinear first kind equation      69
Uniqueness of a solution, nonlinear second kind equation      52 55
Uniqueness of a solution, systems of the second kind      46 62
Unit-impulse function      16
Unit-response function      17
Volterra equations, applications      13
Volterra equations, classification      3
Volterra equations, linear      4
Volterra equations, of first kind      4
Volterra equations, of second kind      3
Volterra population equation      15
Weights for numerical integration      98
Well-posed problems      45
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте