tailieunhanh - Ebook Numerical analysis (2nd edition): Part 2

(BQ) Part 2 book "Numerical analysis" has contents: Boundary value problems, partial differential equations, random numbers and applications, trigonometric interpolation and the FFT, compression, optimization, eigenvalues and singular values. | C H A P T E R 7 Boundary Value Problems Underground and undersea pipelines must be designed to withstand pressure from the outside environment. The deeper the pipe, the more expensive a failure due to collapse will be. The oil pipelines connecting North Sea platforms to the coast lie at a 70-meter depth. The increasing importance of natural gas, and the danger and expense of transportation by ship, may lead to the construction of intercontinental gas pipelines. Mid-Atlantic depths exceed 5 kilometers, where the hydrostatic pressure of 7000 psi will require C innovation in pipe materials and construction to avoid buckling. The theory of pipe buckling is central to a wide array of applications, from architectural supports to coronary stents. Numerical models of buckling are valuable when direct experimentation is expensive and difficult. Reality Check 7 on page 355 represents a cross-sectional slice of a pipe as a circular ring and examines when and how buckling occurs. hapter 6 described methods for calculating the solution to an initial value problem (IVP), a differential equation together with initial data, specified at the left end of the solution interval. The methods we proposed were all “marching’’ techniques—the approximate solution began at the left end and progressed forward in the independent variable t. An equally important set of problems arises when a differential equation is presented along with boundary data, specified at both ends of the solution interval. Chapter 7 describes methods for approximating solutions of a boundary value problem (BVP). The methods are of three types. First, shooting methods are presented, a combination of the IVP solvers from Chapter 6 and equation solvers from Chapter 1. Then, finite difference methods are explored, which convert the differential equation and boundary conditions into a system of linear or nonlinear equations to be solved. The final section is focused on collocation methods and the Finite Element Method, .

• Quản trị mạng
• Numerical analysis
• Boundary value problems
• Partial differential equations
• Trigonometric interpolation
• Random numbers and applications
• Solving equations
• Systems of equations
• Least squares
• Numerical differentiation
• Numerical differentiation and integration
• Mathematical preliminaries
• Error analysis
• Solutions of equations
• Polynomial approximation
• Ordinary differential equations
• Techniques in matrix algebra
• Approximation theory
• Numerical solutions
• Fundamental numerical methods
• Sata analys
• Numerical solution
• Integral equations
• Fourier analysis
• Statistical tests
• Sampling distributions of moments
• Two improved numerical algorithms
• Vibration analysis of systems involving fractional derivatives
• Systems involving fractional derivatives
• Numerical algorithm
• Dynamical systems
• teaching numerical analysis
• techniques
• analysis of results
• mathematics
• systems of nonlinear equations
• matrix algebra
• computer algebra systems
• Large Cavern
• Surrounding rock
• Geotechnical problems
• Tunnel analysis
• Original design calculation
• The internet edition
• Fundamental concepts
• The numerical methods
• Linear equations
• Introduction to spectroscopy
• Numerical solution of ODEs
• Numerical solution of PDEs
• Mathematical introduction
• Discretization methods for PDEs
• Elliptic equations
• Applied numerical methods
• Linear regression
• Polynomial interpolation
• Soil arching
• Numerical simulation
• Piled embankment
• Geosynthetic reinforced pile supported embankment
• 3D numerical modeling
• Advanced materials
• Advanced devices
• Microfluidic platforms
• Cell biology research
• Cell analysis
• Augmented Locking
• Plate Fixation
• Proximal Humeral Fractures
• Comminuted fractures
• Vietnam Journal of Mechanics
• Change in mode shape nodes of multiple cracked bar
• The numerical analysis
• Mode shape node
• Natural modes in axial vibration
• A novel numerical approach
• Fracture analysis in orthotropic media
• Consecutive interpolation procedure
• Two dimensional orthotropic domain
• Stress intensity factor
• A review of available design techniques
• Piled embankment with Geosynthetic
• Available design methods
• Discrete element method
• Experimental and numerical analysis
• The unreinforced
• Reinforced notched timber beam
• Finite element method
• Selftapping screw
• Timber behaviour
• Bifurcation Analysis
• Tracking Control
• Numerical Simulations
• Plasma Edge
• Charge Separation
• Elastic Contact
• Numerical taxonomy
• Numerical classification
• Biogeochemical processes
• Microbiological analysis
• Mycelial fragments
• Technologies
• Averaging
• Conservation of mass
• Multiphase flow models
• Multiphase flow notation
• distribution functions
• Numerical linear algebra
• Solution of nonlinear equations
• Electrical discharge machining
• Mathematical modeling
• Plasma flushing efficiency
• Recast layer thickness
• Discriminant function analysis
• Plantago L
• species
• Plantago taxa
• Hymenopsyllium Pilger
• Numerical analysis of free vibration
• Cross ply thick laminated composite cylindrical shells
• Continuous element method
• The dynamic transfer matrix