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In this volume, we report new results about various boundary value problems for partial differential equations and functional equations, theory and methods of integral equations and integral operators including singular integral equations, applications of boundary value problems and integral equations to mechanics and physics, numerical methods of integral equations and boundary value problems, theory and methods for inverse problems of mathematical physics, Clifford analysis and related problems. Contributors include: L Baratchart, B L Chen, D C Chen, S S Ding, K Q Lan, A Farajzadeh, M G Fei,

Boundary value problems --- Integral equations

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"This Third Edition includes basic modern tools of computational mathematics for boundary value problems and also provides the foundational mathematical material necssary to understand and use the tools. Central to the text is a down-to-earth approach that shows readers how to use differential and integral equations when tackling significant problems in the physical sciences, engineering, and applied mathematics, and the book maintains a careful balance between sound mathematics and meaningful applications. A new co-author, Michael J. Holst, has been added to this new edition, and together he and Ivar Stakgold incorporate recent developments that have altered the field of applied mathematics, particularly in the areas of approximation methods and theory including best linear approximation in linear spaces; interpolation of functions in Sobolev Spaces; spectral, finite volume, and finite difference methods; techniques of nonlinear approximation; and Petrov-Galerkin and Galerkin methods for linear equations. Additional topics have been added including weak derivatives and Sobolev Spaces, linear functionals, energy methods and A Priori estimates, fixed-point techniques, and critical and super-critical exponent problems. The authors have revised the complete book to ensure that the notation throughout remained consistent and clear as well as adding new and updated references. Discussions on modeling, Fourier analysis, fixed-point theorems, inverse problems, asymptotics, and nonlinear methods have also been updated"--

Boundary value problems --- Green's functions --- Mathematical physics

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Boundary value problems --- Differential equations, Elliptic --- Approximation theory. --- Finite element method. --- Numerical solutions.

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This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as of partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which then can be applied to mathematical models of the real world. The problem class includes initial value problems (IVP) for first order differential equations with constant and variable unbounded operator coefficients in a Banach space (the heat equation is a simple example), boundary value problems for the second order elliptic differential equation with an operator coefficient (e.g. the Laplace equation), IVPs for the second order strongly damped differential equation as well as exponentially convergent methods to IVPs for the first order nonlinear differential equation with unbounded operator coefficients.  For researchers and students of numerical functional analysis, engineering and other sciences this book provides highly efficient algorithms for the numerical solution of differential equations and applied problems.

Algebra. --- Boundary value problems -- Textbooks. --- Differential equations, Partial. --- Differential equations. --- Differential equations --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Calculus --- Algorithms. --- 517.91 Differential equations --- Algorism --- Mathematics. --- Mathematics, general. --- Math --- Science --- Algebra --- Arithmetic --- Foundations

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This volume will contain selected papers from the lectures held at the BAIL 2010 Conference, which took place from July 5th to 9th, 2010 in Zaragoza (Spain). The papers present significant advances in the modeling, analysis and construction of efficient numerical methods to solve boundary and interior layers appearing in singular perturbation problems. Special emphasis is put on the mathematical foundations of such methods and their application to physical models. Topics in scientific fields such as fluid dynamics, quantum mechanics, semiconductor modeling, control theory, elasticity, chemical reactor theory, and porous media are examined in detail.

Boundary layer -- Congresses. --- Boundary layer. --- Boundary value problems -- Asymptotic theory -- Congresses. --- Boundary value problems. --- Boundary layer --- Boundary value problems --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Applied Mathematics --- Mathematics - General --- Asymptotic theory --- Computational steering (Computer science) --- Boundary conditions (Differential equations) --- Steering, Computational (Computer science) --- Mathematics. --- Computer mathematics. --- Applied mathematics. --- Engineering mathematics. --- Fluid mechanics. --- Computational Mathematics and Numerical Analysis. --- Appl.Mathematics/Computational Methods of Engineering. --- Engineering Fluid Dynamics. --- Hydromechanics --- Continuum mechanics --- Engineering --- Engineering analysis --- Mathematical analysis --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Math --- Science --- Computer programs --- Software visualization --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Execution --- Management --- Computer science --- Hydraulic engineering. --- Mathematical and Computational Engineering. --- Engineering, Hydraulic --- Fluid mechanics --- Hydraulics --- Shore protection