 Sewell, Granville, author.
 Hoboken, NJ : John Wiley & Sons, Inc., 2018.
 Description
 Book — 1 online resource (1 volume) : illustrations
 Summary

 Preface vii
 I Introduction to PDE2D 1
 I.1 The Collocation and Galerkin Finite Element Methods 1
 I.2 The PDE2D User Interfaces 7
 I.3 Accuracy 11
 I.4 Computer Time and Memory 13
 I.5 Programming Hints 17
 1 The Damped Spring and Pendulum Problems 21
 1.1 Derivation of the Damped Spring and Pendulum Equations 21
 1.2 Damped Spring and Pendulum Examples 23
 1.3 Problems 24
 2 Beam and Plate Bending 31
 2.1 Derivation of Beam Bending Equation 31
 2.2 Derivation of Plate Bending Equation 32
 2.3 Beam and Plate Examples 33
 2.4 Problems 34
 3 Diffusion and Heat Conduction 39
 3.1 Derivation of Diffusion Equation 39
 3.2 Diffusion and Heat Conduction Examples 40
 3.3 Problems 51
 4 Pricing Options 61
 4.1 Derivation of BlackScholes Equation 61
 4.2 Option Pricing Examples 65
 4.3 Problems 70
 5 Elasticity 75
 5.1 Derivation of Elasticity Equations 75
 5.2 Elasticity Examples 77
 5.3 Problems 81
 6 Incompressible Fluid Flow 95
 6.1 Derivation of NavierStokes Equations 95
 6.2 Stream Function and PenaltyMethod Approaches 97
 6.3 Fluid Flow Examples 97
 6.4 Problems 105
 7 The Schroedinger and Other Eigenvalue Equations 119
 7.1 The Schroedinger Equation 119
 7.2 Schroedinger and Maxwell Equations Examples 119
 7.3 Problems 126
 8 Minimal Surface and MembraneWave Equations 137
 8.1 Derivation of Minimal Surface Equation 137
 8.2 Derivation of MembraneWave Equation 138
 8.3 Examples 140
 8.4 Problems 142
 9 The KPIWave Equation 149
 9.1 A Difficult Nonlinear Problem 149
 9.2 Numerical Results 155
 Appendix A: Formulas from Multivariate Calculus 161
 Appendix B: Algorithms Used by PDE2D 163
 Appendix C: Equations Solved by PDE2D 183
 Appendix D: Problem 5.7 Local Solvers 193
 References 205
 Index 207.
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63. Numerical models for differential problems [2017]
 Quarteroni, Alfio, author.
 Third edition.  Cham, Switzerland : Springer, [2017]
 Description
 Book — xvii, 681 pages : illustrations (some color) ; 25 cm.
 Summary

 1 A brief survey of partial differential equations. 2 Elements of functional analysis. 3 Elliptic equations. 4 The Galerkin finite element method for elliptic problems. 5 Parabolic equations. 6 Generation of 1D and 2D grids. 7 Algorithms for the solution of linear systems. 8 Elements of finite element programming. 9 The finite volume method. 10 Spectral methods. 11 Isogeometric analysis. 12 Discontinuous element methods (D Gandmortar). 13 Diffusiontransportreaction equations. 14 Finite differences for hyperbolic equations. 15 Finite elements and spectral methods for hyperbolic equations. 16 Nonlinear hyperbolic problems. 17 NavierStokes equations. 18 Optimal control of partial differential equations. 19 Domain decomposition methods. 20 Reduced basis approximation for parametrized partial differential equations. References.
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QA377 .Q375 2017  Unknown 
64. Fourier series and numerical methods for partial differential equations [electronic resource] [2010]
 Bernatz, Richard, 1955
 Hoboken, N.J. : Wiley, c2010.
 Description
 Book — 1 online resource (xiii, 318 p.) : ill.
 Summary

 Preface. Acknowledgments. 1 Introduction. 1.1 Terminology and Notation. 1.2 Classification. 1.3 Canonical Forms. 1.4 Common PDEs. 1.5 Cauchy Kowalevski Theorem. 1.6 Initial Boundary Value Problems. 1.7 Solution Techniques. 1.8 Separation of Variables. Exercises. 2 Fourier Series. 2.1 Vector Spaces. 2.2 The Integral as an Inner Product. 2.3 Principle of Superposition. 2.4 General Fourier Series. 2.5 Fourier Sine Series on (0, c). 2.6 Fourier Cosine Series on (0, c). 2.7 Fourier Series on ( c
 c). 2.8 Best Approximation. 2.9 Bessel's Inequality. 2.10 Piecewise Smooth Functions. 2.11 Fourier Series Convergence. 2.12 2cPeriodic Functions. 2.13 Concluding Remarks. Exercises. 3 Sturm Liouville Problems. 3.1 Basic Examples. 3.2 Regular Sturm Liouville Problems. 3.3 Properties. 3.4 Examples. 3.5 Bessel's Equation. 3.6 Legendre's Equation. Exercises. 4 Heat Equation. 4.1 Heat Equation in 1D. 4.2 Boundary Conditions. 4.3 Heat Equation in 2D. 4.4 Heat Equation in 3D. 4.5 PolarCylindrical Coordinates. 4.6 Spherical Coordinates. Exercises. 5 Heat Transfer in 1D. 5.1 Homogeneous IBVP. 5.2 Semihomogeneous PDE. 5.3 Nonhomogeneous Boundary Conditions. 5.4 Spherical Coordinate Example. Exercises. 6 Heat Transfer in 2D and 3D. 6.1 Homogeneous 2D IBVP. 6.2 Semihomogeneous 2D IBVP. 6.3 Nonhomogeneous 2D IBVP. 6.4 2D BVP: Laplace and Poisson Equations. 6.5 Nonhomogeneous 2D Example. 6.6 TimeDependent BCs. 6.7 Homogeneous 3D IBVP. Exercises. 7 Wave Equation. 7.1 Wave Equation in 1D. 7.2 Wave Equation in 2D. Exercises. 8 Numerical Methods: an Overview. 8.1 Grid Generation. 8.2 Numerical Methods. 8.3 Consistency and Convergence. 9 The Finite Difference Method. 9.1 Discretization. 9.2 Finite Difference Formulas. 9.3 1D Heat Equation. 9.4 Crank Nicolson Method. 9.5 Error and Stability. 9.6 Convergence in Practice. 9.7 1D Wave Equation. 9.8 2D Heat Equation in Cartesian Coordinates. 9.9 TwoDimensional Wave Equation. 9.10 2D Heat Equation in Polar Coordinates. Exercises. 10 Finite Element Method. 10.1 General Framework. 10.2 1D Elliptical Example. 10.3 2D Elliptical Example. 10.4 Error Analysis. 10.5 1D Parabolic Example. Exercises. 11 Finite Analytic Method. 11.1 1D Transport Equation. 11.2 2D Transport Equation. 11.3 Convergence and Accuracy. Exercises. Appendix A: FA 1D Case. Appendix B: FA 2D Case. References. Index.
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65. Numerical partial differential equations [2010]
 Thomas, J. W. (James William), 1941
 New York : Springer, [2010]
 Description
 Book — 1 online resource (xx, 436 pages) : illustrations
 Summary

 Introduction to Finite Difference. Some Theoretical Considerations. Stability. Parabolic Equations. Hyperbolic Equations. Systems of Partial Differential Equations. Dispersion and Dissipation. References. Index.
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66. Numerical models for differential problems [2009]
 Modellistica numerica per problemi differenziali. English
 Quarteroni, Alfio.
 Milan ; New York : Springer, ©2009.
 Description
 Book — 1 online resource (xvi, 601 pages) : illustrations Digital: text file.PDF.
 Summary

 A brief survey on partial differential equations. Elements of functional analysis. Elliptic equations. The Galerkin finite element method for elliptic problems. Parabolic equations. Generation of 1D and 2D grids. Algorithms for the solution of linear systems. Elements of finite element programming. The finite volume method. Spectral methods. Diffusiontransportreaction equations. Finite differences for hyperbolic equations. Finite elements and spectral methods for hyperbolic equations. Nonlinear hyperbolic problems. NavierStokes equations. Optimal control of partial differential equations. Domain decomposition methods. Reduced basis approximation for parametrized partial differential equations.
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 Mathew, Tarek P. A. (Tarek Poonithara Abraham)
 Berlin : Springer, c2008.
 Description
 Book — xiii, 764 p. : ill.
 Gustafsson, Bertil, 1930
 Berlin : Springer, c2008.
 Description
 Book — xv, 334 p. : ill. ; 24 cm.
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QA377 .G88 2008  Unknown 
 Gustafsson, Bertil, 1930
 Berlin : Springer, 2008.
 Description
 Book — xv, 334 p. : ill.
70. Realtime PDEconstrained optimization [2007]
 Philadelphia : Society for Industrial and Applied Mathematics, c2007.
 Description
 Book — xxiii, 312 p. : ill. (some col.) ; 26 cm.
 Summary

 Preface
 Part I. Concepts and Properties of RealTime, Online Strategies: 1. Constrained optimal feedback control for DAE
 2. A stabilizing realtime implementation of NMPC
 3. Numerical feedback controller design for PDE systems using model reduction: techniques and case studies
 4. Leastsquares methods for optimization
 Part II. Fast PDEConstrained Optimization Solvers: 5. Spacetime multigrid methods for solving unsteady optimal control problem
 6. A timeparallel implicit methodology for the nearrealtime solution of systems of linear oscillators
 7. Generalized SQPmethods with 'parareal' timedomain decomposition for timedependent PDEconstrained optimization
 8. Simultaneous pseudotimestepping for state constrained optimization problems in aerodynamics
 9. The effect of the digital filter stepsize control on control optimization performance
 Part III. Reduced Order Modeling: 10. Certified rapid solution of partial differential equations for realtime parameter estimation and optimization
 11. WillcoxMOR
 12. Feedback control of flow separation
 Part IV. Applications: 13. Shape and topological sensitivity
 14. COFIR: Coarse and fine image registration
 15. Realtime, large scale optimization of water network systems using a subdomain approach
 Index.
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QA402.5 .R41 2007  Unknown 
 Quarteroni, Alfio.
 3a ed.  Milan : SpringerVerlag, 2006.
 Description
 Book — xiii, 451 p. : ill.
 Lagnese, J.
 Basel ; Boston : Birkhäuser Verlag, c2004.
 Description
 Book — xiii, 443 p. : ill. ; 24 cm.
 Summary

 Preface.
 1. Introduction.
 2. Background Material on Domain Decomposition.
 3. Partial Differential Equations on Graphs.
 4. Optimal Control of Elliptic Problems.
 5. Control of Partial Differential Equations on Graphs.
 6. Control of Dissipative Wave Equations.
 7. Boundary Control of Maxwell's System.
 8. Control of Conservative Wave Equations.
 9. Domain Decomposition for 2DNetworks. Bibliography. Index.
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QA297 .I5 V.148  Unknown 
73. Largescale PDEconstrained optimization [2003]
 Berlin ; New York : Springer, 2003.
 Description
 Book — vi, 349 p. : ill. (some col.) ; 24 cm.
 Summary

Optimal design, optimal control, and parameter estimation of systems governed by partial differential equations (PDEs) give rise to a class of problems known as PDEconstrained optimization. The size and complexity of the discretized PDEs often pose significant challenges for contemporary optimization methods. With the maturing of technology for PDE simulation, interest has now increased in PDEbased optimization. The chapters in this volume collectively assess the state of the art in PDEconstrained optimization, identify challenges to optimization presented by modern highly parallel PDE simulation codes, and discuss promising algorithmic and software approaches for addressing them. These contributions represent current research of two strong scientific computing communities, in optimization and PDE simulation. This volume merges perspectives in these two different areas and identifies interesting open questions for further research.
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QA402.5 .L358 2003  Unknown 
 Prakticheskiĭ kurs po uravnenii͡am matematicheskoĭ fiziki. English
 Pikulin, V. P. (Viktor Pavlovich)
 Basel ; Boston : Birkhäuser Verlag, c2001.
 Description
 Book — viii, 206 p. : ill. ; 24 cm.
 Summary

Mathematical modeling and numerical simulation in fluid mechanics are topics of great importance both in theory and technical applications. The present book attempts to describe the current status in various areas of research. The 10 chapters, mostly survey articles, are written by internationally renowned specialists and offer a range of approaches to and views of the essential questions and problems. In particular, the theories of incompressible and compressible NavierStokes equations are considered, as well as stability theory and numerical methods in fluid mechanics. Although the book is primarily written for researchers in the field, it will also serve as a valuable source of information to graduate students.
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QC20.7 .D5 P55 2001  Available 
 Singapore ; River Edge, N.J. : World Scientific Pub. Co., c2000.
 Description
 Book — xii, 250 p. : ill.
 Summary

 Nonstandard finite difference schemes, R.E. Mickens
 nonstandard methods for advectiondiffusionreaction equations, H.V. Kojouharov and B.M. Chen
 application of nonstandard finite differences to solve the wave equation and Maxwell's equations, J.B. Cole
 nonstandard discretization methods for some biological models, H. AlKahby et al
 an introduction to numerical integrators preserving physical properties, M.J. Gander and R. MeyerSpasche.
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 Li, Ronghua.
 New York : M. Dekker, c2000.
 Description
 Book — xv, 442 p. : ill. ; 24 cm.
 Summary

 Preliminaries
 two point boundary value problems
 second order elliptic equations
 fourth order and nonlinear elliptic equations
 parabolic equations
 hyperbolic equations
 convectiondominated diffusion problems
 applications.
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QA431 .L575 2000  Available 
 Quarteroni, Alfio.
 Oxford : Clarendon Press ; New York : Oxford University Press, 1999.
 Description
 Book — xv, 360 p. : ill. ; 24 cm.
 Summary

 1. Mathematical foundation of domain decomposition methods
 2. Discretized equations and domain decomposition
 3. Iterative domain decomposition methods at the discrete level
 4. Convergence analysis for iterative domain decomposition
 5. Other boundary value problems
 6. Advectiondiffusion equations
 7. Timedependent problems
 8. Heterogeneous domain decomposition methods.
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QA377 .Q34 1999  Unknown 
 San Diego : Academic Press, 1997.
 Description
 Book — xiv, 570 p. : ill.
 Summary

 FEMLike Multilevel Preconditioning: P. Oswald, Multilevel Solvers for Elliptic Problems on Domains. P. Vassilevski and J. Wang, WaveletLike Methods in the Design of Efficient Multilevel Preconditioners for Elliptic PDEs. Fast Wavelet Algorithms: Compression and Adaptivity: S. Bertoluzza, An Adaptive Collocation Method Based on Interpolating Wavelets. G. Beylkin and J. Keiser, An Adaptive PseudoWavelet Approach for Solving Nonlinear PartialDifferential Equations. P. Joly, Y. Maday, and V. Perrier, A Dynamical Adaptive Concept Based on Wavelet Packet Best Bases: Application to Convection Diffusion Partial Differential Equations. S. Dahlke, W. Dahmen, and R. DeVore, Nonlinear Approximation and Adaptive Techniques for Solving Elliptic Operator Equations. Wavelet Solvers for Integral Equations: T. von Petersdorff and C. Schwab, Fully Discrete Multiscale Galerkin BEM. A. Rieder, Wavelet Multilevel Solvers for Linear IllPosed Problems Stabilized by Tikhonov Regularization. Software Tools and Numerical Experiments: T. Barsch, A. Kunoth, and K. Urban, Towards Object Oriented Software Tools for Numerical Multiscale Methods for PDEs Using Wavelets. J. Ko, A. Kurdila, and P. Oswald, Scaling Function and Wavelet Preconditioners for Second Order Elliptic Problems. Multiscale Interaction and Applications to Turbulence: J. Elezgaray, G. Berkooz, H. Dankowicz, P. Holmes, and M. Myers, Local Models and Large Scale Statistics of the KuramotoSivashinsky Equation. M. Wickerhauser, M. Farge, and E. Goirand, Theoretical Dimension and the Complexity of Simulated Turbulence. Wavelet Analysis of Partial Differential Operators: JM. Angeletti, S. Mazet, and P. Tchamitchian, Analysis of SecondOrder Elliptic Operators Without Boundary Conditions and With VMO or Hilderian Coefficients. M. Holschneider, Some Directional Elliptic Regularity for Domains with Cusps. Subject Index.
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 Shashkov, Mikhail.
 Boca Raton : CRC Press, 1996.
 Description
 Book — 359 p, : ill. ; 24 cm. + 1 computer disk (3 1/2 in.)
 Summary

 INTRODUCTION Governing Equations Elliptic Equations Heat Equation Equation of Gas Dynamic in Lagrangian Form The Main Ideas of FiniteDifference Algorithms 1D Case 2D Case Methods of Solution of Systems of Linear Algebraic Equation Methods of Solution of Systems of Nonlinear Equations METHOD OF SUPPORTOPERATORS Main Stages The Elliptic Equations Gas Dynamic Equations System of Consistent Difference Operators in 1D Inner Product in Spaces of Difference Functions and Properties of Difference Operators System of Consistent Difference Operators in 2D THE ELLIPTIC EQUATIONS Introduction Continuum Elliptic Problems with Dirichlet Boundary Conditions Continuum Elliptic Problems with Robin Boundary Conditions OneDimensional Support Operator Algorithms Nodal Discretization of Scalar Functions and CellCentered Discretization of Vector Functions CellValued Discretization of Scalar Functions and Nodal Discretization of Vector Functions Numerical Solution of Test Problems TwoDimensional Support Operator Algorithms Nodal Discretization of Scalar Functions and CellValued Discretization of Vector Functions CellValued Discretization of Scalar Functions and Nodal Discretization of Vector Functions Numerical Solution of Test Problems Conclusion TwoDimensional Support Operator Algorithms Discretization Spaces of Discrete Functions The Prime Operator The Derived Operator Multiplication by a Matrix and the Operator D The Difference Scheme for the Elliptic Operator The Matrix Problem Approximation and Convergence Properties HEAT EQUATION Introduction FiniteDifference Schemes for Heat Equation in 1D FiniteDifference Schemes for Heat Equation in 2D LAGRANGIAN GAS DYNAMICS Kinematics of Fluid Motions Integral Form of Gas Dynamics Equations Integral Equations for One Dimensional Case Differential Equations of Gas Dynamics in Lagrangian Form The Differential Equations in 1D. Lagrange Mass Variables The Statements of Gas Dynamics Problems in Lagrange Variables Different Forms of Energy Equation Acoustic Equations Reference Information Characteristic Form of Gas Dynamics Equations Riemann's Invariants Discontinuous Solutions Conservation Laws and Properties of First Order Invariant Operators FiniteDifference Algorithm in 1D Discretization in 1D Discrete Operators in 1D SemiDiscrete FiniteDifference Scheme in 1D Fully Discrete, Explicit, Computational Algorithm Computational AlgorithmNew Time StepExplicit FiniteDifference Scheme Computational AlgorithmNew Time StepImplicit FiniteDifference Scheme Stability Conditions Homogeneous FiniteDifference Schemes. Artificial Viscosity Artificial Viscosity in 1D Numerical Example Finite Difference Algorithm in 2D Discretization in 2D Discrete Operators in 2D SemiDiscrete FiniteDifference Scheme in 2D Stability Conditions FiniteDifference Algorithm in 2D Computational AlgorithmNew Time StepExplicit FiniteDifference Scheme Computational AlgorithmNew Time StepImplicit FiniteDifference Scheme Artificial Viscosity in 2D Numerical Example APPENDIX: FORTRAN CODE DIRECTORY General Description of Structure of Directories on the Disk Programs for Elliptic Equations Programs for 1D Equations Programs for 2D Equations Programs for Heat Equations Programs for 1D Equations Programs for 2D Equations Programs for Gas Dynamics Equations Programs for 1D Equations Programs for 2D Equations Bibliography.
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QA431 .S484 1996  Available 
80. Numerical partial differential equations [1995  1999]
 Thomas, J. W. (James William), 1941
 New York : Springer, c1995c1999.
 Description
 Book — 2 v. : ill. ; 25 cm.
 Summary

 [1] Finite difference methods
 [2] Conservation laws and elliptic equations.
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Of the many different approaches to solving partial differential equations numerically, this book studies difference methods. Written for the beginning graduate student in applied mathematics and engineering, this text offers a means of coming out of a course with a large number of methods that provide both theoretical knowledge and numerical experience. The reader will learn that numerical experimentation is a part of the subject of numerical solution of partial differential equations, and will be shown some uses and taught some techniques of numerical experimentation.Prerequisites suggested for using this book in a course might include at least one semester of partial differential equations and some programming capability. The author stresses the use of technology throughout the text, allowing the student to utilize it as much as possible. The use of graphics for both illustration and analysis is emphasized, and algebraic manipulators are used when convenient. This is the second volume of a twopart book.
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QA377 .T495 1995 V.1  Unknown 
QA377 .T495 1995 V.2  Unknown 
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