Додатковий титульний аркуш українською мовою

01356287 Дар Академперіодики

Бібліографія: сторінки 148-153 (73 назви)

PREFACE.....7
CHAPTER 1
IMPLICATION OF STRUCTURAL METHODS FOR MATHEMATICAL AND COMPUTER MODELING OF PHYSICAL AND MECHANICAL FIELDS
1.1. R- function method.....11
1.2. Analysis of some constructive means of R-function theory.....13
1.3. Normalization of R-operations.....16
1.4. Computational scheme of R-function method.....21
CHAPTER 2
NEW CONSTRUCTIVE METHODS OF DESCRIPTION OF AREAS OF COMPLEX SHAPE BASED ON THE STUDY OF BEHAVIOR OF SMOOTH FUNCTIONS ACQUIRING CONSTANT VALUES ON NON-SMOOTH CURVES
2.1. Corners rounding when describing areas with a non-smooth border.....27
2.2. R-operation systems for different smoothness classes..... 31
2.3. Behavior of smooth functions with constant values on non-smooth curves in the vicinity of the corner point.....47
2.4. New system of R-operations.....56
CHAPTER 3
METHOD OF CONSTRUCTION OF BORDER BASIC ELEMENTS BASED ON CUBIC B-SPLINES
3.1. Construction of boundary basic elements for one-dimensional boundary value problems with different boundary conditions.....73
3.2. Construction of boundary basic elements for approximation of functions satisfying the homogeneous Dirichlet boundary condition in the two-dimensional case......81
3.3. Software description.....88
CHAPTER 4
PROBLEMS OF APPROXIMATION WITH THE USE OF DEVELOPED STRUCTURES OF BORDER PROBLEMS SOLUTIONS
4.1. Solution structures usage for functions approximation.....91
4.1.1. Approximation of smooth function f (x, y)= x, y.....91
4.1.2. Approximation of the function f(x, y) =f11(x, y)f12(x, y).....91
4.2. Implication of structures for analysis of boundary value problems solutions approximation ability.....95
4.2.1. A model example of a boundary value problem.....95
4.2.2. Approximation of a function from the system of R-operations Rk.....97
4.2.3. Test boundary value problem that has an analytical solution.....101
4.2.4. Implication of boundary basic elements to solve boundary value problems.....102
4.3. Examples of some boundary value problems solving.....105
4.3.1. Torsion of a square prism.....105
4.3.2. Solution of a real practical problem.....107
CHAPTER 5
MATHEMATICAL AND COMPUTER MODELING OF HYDRODYNAMIC
5.1. Mathematical modeling of hydrodynamic processes using the R-function method for flat channels.....113
5.1.1. Problem statement for the velocity field.....113
5.1.2. Problem statement for the static pressure field.....114
5.1.3. Implementation examples.....117
5.2. Mathematical modeling of viscous incompressible fluid flow along axisymmetric channels of the complex cross-section using the
R-function method.....136
5.2.1. Problem statement for the velocity field.....136
5.2.2. Problem statement for the static pressure field.....140
5.2.3. Mathematical modeling ofhydrodynamic processes in the model channel of the hydro vortex nozzle.....143
REFERENCES.....148
AUTHORS.....154

The monograph presents the development of structural methods to increase the approximation capacity of basis functions in the vicinity of the corner points of the area to solve boundary value problems and also the development of local structures that take into account boundary conditions at the area border and docking with standard basis within the area. The development of structural methods based on the approaches listed above significantly expands the possibilities of physical and mechanical processes modeling in the areas of complex shapes to create environmental and economic devices in various industries.