| Description |
1 online resource (xvi, 601 pages) : illustrations |
| Series |
MS & A ; v. 2 |
|
MS & A (Series) ; v. 2
|
| Contents |
Introduction -- 1 A brief survey on partial differential equations -- 2 Elliptic equations -- 3 The Galerkin finite element method for elliptic problems -- 4 Spectral methods -- 5 Diffusion-transport-reaction equations -- 6 Parabolic equations -- 7 Finite differences for hyperbolic equations -- 8 Finite elements and spectral methods for hyperbolic equations -- 9 Nonlinear hyperbolic problems -- 10 The Navier-Stokes equations -- 11 Finite element programming -- 12 Generation of 1D and 2D grids -- 13 The finite volume method -- 14 Domain decomposition method -- 15 Optimal control problems for partial differential equations -- 16 Reduced basis methods -- 17 Appendix A: Elements of functional analysis -- 18 Appendix B: Solution of algebraic systems |
| Summary |
In this text, we introduce the basic concepts for the numerical modelling of partial€ differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods.€ In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
|
Print version record |
| Subject |
Differential equations, Partial -- Numerical solutions.
|
|
Numerical analysis.
|
|
Differential equations, Partial -- Numerical solutions.
|
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Numerical analysis.
|
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Differential equations, Partial -- Numerical solutions
|
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Numerical analysis
|
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Numerisches Verfahren
|
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Partielle Differentialgleichung
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Numerisk analys.
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Numeriska metoder.
|
| Form |
Electronic book
|
| LC no. |
2009922766 |
| ISBN |
9788847010710 |
|
8847010713 |
|
9783319493169 |
|
3319493167 |
|
