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Agoshkov V.I., Dubovsky P.B. — Methods for Solving Mathematical Physics Problems
Agoshkov V.I., Dubovsky P.B. — Methods for Solving Mathematical Physics Problems



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Название: Methods for Solving Mathematical Physics Problems

Авторы: Agoshkov V.I., Dubovsky P.B.

Аннотация:

The book examines the classic and generally accepted methods for solving mathematical physics problems (method of the potential theory, the eigenfunction method, integral transformation methods, discretisation characterisation methods, splitting methods). A separate chapter is devoted to methods for solving nonlinear equations. The book offers a large number of examples of how these methods are applied to the solution of specific mathematical physics problems, applied in the areas of science and social activities, such as energy, environmental protection, hydrodynamics, theory of elasticity, etc.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 330

Добавлена в каталог: 21.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adjoint nonlinear operators      279
Alternating-direction method      252
Approximation requirement      164
Arzela — Ascoli theorem      6
Banach space      1 5 6 206
Bessel inequality      12 101
Bochner transform      131 141
Boundary of the domain      4
Boundary-value conditions      33
Boundary-value conditions of the first kind      98
Boundary-value conditions of the third kind      98
Boundary-value problem      33
Bubnov — Galerkin method      201
Cauchy problem      3 33 225
Cauchy — Bunyakovskii inequality      10 46
Cauchy — Kovalevskii theorem      37
Characteristic function      4
Chebyshef polynomial      107
Chernov formula      230
Chezy coefficient      264
Class of functions      4
Closed linear operator      16
Coercivity condition      283
Collocation method      208
Compact set      5
Completeness equation      12
Convergence in respect to energy      16
Convergence theorem      173 240
Convolution transform      131
Coriolis parameter      264
Courant method      196
Cranck — Nicholson scheme      238
Cylindrical coordinates      58
Cylindrical function      106
d'Alembert operator      2 26
Differential operator      15
diffusion length      150
Dipole coefficient      67
Direct methods      189
Dirichlet boundary condition      23
Dirichlet integral      2 38
Dirichlet problem      38 71
Discrete Laplace transform      130
Domain of definition of the equation      32
Dubois — Raymond lemma      19
Eigen subspace      18
Eigenfunction      97
eigenvalue problems      94
Energetic space      16
Energy method      46
Energy space      192
Equation of state      29
Equations of continuity      29
Euclidean distance      3
Euclidean space      3 11
Euler equation      104
Euler equation of motion      29
Evolution equations      225
Factorisation method      169
Finite-difference methods      166
First Green formula      60
Fourier coefficient      101
Fourier map      132
Fourier series      10
Fourier transform      133
Fourier — Bessel integral      136
Frechet derivative      278
Frechet differential      278
Fredholm equation      2 73
Fredholm integral equation      50
Functional of the energy method      46
Galerkin approximation      294
Galerkin method      201
Galerkin — Petrov method      201
Gateaux derivative      277
Gauss hypergeometrical series      109
Generalized derivatives      19
Generalized Minkovskii inequality      9
Generalized solutions      37
Generating function      160
Gilbert transform      131
Green formula      21 40
Green function      76 84
Haar system      142
Hankel function      107
Hankel image      146
Hankel transform      131 136
Hardy inequality      9
Heat conductivity equation      27
Helmholtz equation      26
Hermite polynomial      108
Hermitian weakly polar kernel      54
Hilbert spaces      9
Hilbert transform      140
Hilbert — Schmidt orthogonalization      12
Hilbert — Schmidt theorem      54
Hoelder function      1
Hoelder inequality      9
Hoelder space      7
Hyperbolicity condition      32
Hyperplane method      183
Ill-posed problem      36
Integral Green formula      60
Internal point of the set      3
Internal spherical functions      104
Isometric space      5
Isomorphous space      5
Jump of the normal derivative      66
Kantorovich method      196
Kellog theorem      240
Kernel      14
Kinetic coagulation equation      159
Kontorovich — Lebedev transform      131 138
Kummer function      109
Laguerre polynomial      108
Laguerre transform      131
Laplace equation      23
Laplace operator      2 59
Laplace — Beltrami operator      105
Law of oscillation      96
Lebesgue integral      7
Lebesgue space      7
Legendre polynomial      105
Legendre transform      131
Linear functional      14
Linear normalised space      5
Linear operator      13
Linear sets      5
Lipschits condition      4
Lipschitz inequality      277
Logarithmic potential      63
Logarithmic simple layer potential      66
Longitudinal–transverse sweep      252
Lyapunov surface      65 76
Macdonald function      138
Mathieu equation      109
Mathieu function      109
Maxwell equations      27
Mehler — Fock transform      131
Meller — Fock transform      139
Mellin transform      131
Method of arbitrary lines      182
Method of eigenfunctions      232
Method of Gauss exclusion      169
Method of integral identities      210
Method of least squares      195
Method of Marchuk's integral identity      211
Method of stationarisation      232
Method of two-cyclic multi-component splitting      245
Method of weak approximation      254
Meyer transform      138
Minimising sequence      190
Mixed problem      33
Moments method      204
Multiplicity      17
Navier — Stokes equation      262
Neighbourhood of the set      3
Net method      166
Neumann condition      23
Neumann problem      34 40 48
Newton iteration process      291
Newton potential      61
Nonhomogeneous evolution equation      228
Normalized eigenfunction      100
One-dimensional wave equation      24
Oriented surface      67
Orthogonal basis      10
Orthogonal system      10
Orthonormalized system      10
Ostrogradskii — Gauss formula      60
Parseval equality      102
Parseval identity      134
Parseval — Steklov equality      12
Periodicity conditions      99
Piecewise smooth surface      4
Poincare inequality      41
Poincare — Perron method      80
Point spectrum      18
Poisson equation      23
Poisson integral      73
Potential of the vector field      57
Predictor-corrector method      250
Problem of a string      124
Projection method      205
Projection-grid method      208
Quadrature method      187
Reflexive real Banach space      283
Reiss — Fischer theorem      11
Retardation time      92
Riesz theorem      8 41 46
Ritz method      190 289
Rodrig formula      106
Schmidt equation      54
Schwarz method      78
Second Green formula      60
Second Hankel function      82
Simple eigenvalue      18 97
Simple layer potential      64
Sobolev classes      20
Sobolev space      1 19
Special functions      103
Spherical coordinates      58
Spherical function      103
Splitting method      225 242
Stability      239
Standing wave      96
Steepest descent method      286
Stricker coefficient      264
Struve function      137
Sturm — Liouville operator      103
Super-harmonic function      80
Support      5
Sweep method      169 241
Sweeping method      80
Symmetric hyperbolic systems      32
Symmetric kernel      54
The minimisation condition J(uN) leads to a system      195
Three-dimensional wave equation      25
Transfer equation      28
Trefftz method      197
Tricomi equation      31
Trotter formula      230
Two-cyclic method of weak approximation      254
Two-dimensional wave equation      25
Variational formulation of problems      45
Variational method      283
Volterra equation      89
Wavelet integral transform      142
Wavelet transform      131
Weakly polar kernel      51
Weber transform      137
Weierstrass theorem      6 11
Weierstrasse theorem      282
Weight function      99
Young inequality      9
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