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Shapira Y. — Solving PDEs in C++: numerical methods in a unified object-oriented approach
Shapira Y. — Solving PDEs in C++: numerical methods in a unified object-oriented approach



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Название: Solving PDEs in C++: numerical methods in a unified object-oriented approach

Автор: Shapira Y.

Аннотация:

This book teaches C++ and uses it to solve partial differential equations (PDEs). Basic and advanced numerical methods are introduced and implemented easily and efficiently in a unified object-oriented approach.
The powerful features and advanced tools available in C++ are particularly useful for implementing the complex mathematical objects that are often used in numerical modeling. The code segments and their detailed explanations show how easy it is to implement advanced algorithms such as finite elements and multigrid.
The book contains such as six parts. The first two parts introduce C, C++, and the object-oriented approach. The third and fourth parts describe and implement finite-difference and finite-element schemes. The fifth part deals with numerical linear algebra and parallelism. The sixth and final part uses the present approach in advanced applications. Each chapter ends with exercises and solutions.
The book contains two theoretical chapters, which can be skipped by readers who are interested in only the practical aspects (Chapters 8 and 11 and also Sections 9.9, 12.7, 18.16, and 20.4-20.5). More advanced readers may find them most useful and relevant to the present methods.
Because the book already contains the required background in programming, PDEs, and numerical methods, the only prerequisites are calculus and linear algebra. It can thus be used as a textbook in courses on C++ for scientific computing, C++ for engineers, numerical analysis, and numerical PDEs in the advanced undergraduate and graduate levels. Because it is self-contained, it is also suitable for self-study by researchers and students in applied and computational sciences and engineering.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 524

Добавлена в каталог: 29.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
String, as input      36
String, to copy a      36
String, to print a      13 25
Strong formulation      251
Strong formulation, in elasticity      403
Subshape      128
Subspace, invariant      164
Subspace, invariant, stable      164
Subspace, Krylov      359 360 470 474
Symmetric, bilinear form      251 256
Symmetric, differencing      188 192
Symmetric, matrix      122
Symmetric, PDE      247
Symmetric, stiffness matrix      261 262 421
system      193 see “Linear
Task, assigning      375
Task, computational      3 369
Task, modularity in      4
Task, recursion in      36
Taylor, approximation      90
Taylor, error      148 169
Taylor, expansion      40 148
Taylor, polynomial      40
Taylor, scheme      167 170 172 176
template      72 94
Template, in dynamic vector      95
tetrahedron      279 286 290
TFQMR      362 472
This see “"this"”      56
Time level      190 211 399 444
Time marching      190 212 399 see “Semi-implicit
Time step      190 211
Time, exponential      3
Time, polynomial      3 4
Time-space domain      181 see
Time-space grid      199 see
Toeplitz matrix      276
TREE      112
Triangulation      128 259
Turing      3
Turing, machine      3 136
TYPE      7 see
typedef      78 see
Uncomputable problem, practically      3
Uniqueness      255
Unsolvable problem, practically      3
Unstructured mesh      281 see
Upwind scheme      189
Variable      7 15
Variable, concrete      17 see
Variable, local      12 16 58
Variable, local, in constructor      54
Variable, local, in function      40
Variable, local, in loop      19
Variable, local, return      59 66 350
Variable, local, returned      70
Variable, pass by address      57
Vector      75 111 439
Vector, dynamic      94 111 442
Virtual address      121 see
void      11 12
von Neumann      3
Wave equation      425
Weak formulation      250
Weak formulation, discrete      260
Weak formulation, in elasticity      404
Weak sense      220
Well-posed      251 252 259
Well-posed, in elasticity      404 405
while      17 see
WRITE      13 see “"fprintf"”
1 2 3 4
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