Stable computations by discrete mollification

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Stable computations by discrete mollification

Libro Impreso

40000

Disponibilidad: Disponible


Categoría: Matemática

Editorial: Universidad Nacional de Colombia

Universidad Nacional de Colombia

Año de Edición: 2014

2014

ISBN: 9789587617535

9789587617535

Sede: Bogotá


The discrete mollification method is a data smoothing procedure, based on convolution, that is appropriate for the stabilization of explicit schemes for the numerical solution of partial differential equations and the regularization of ill-posed problems. This text introduces some of the main result...
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COP $ 40.000
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SKU: 235960

Producto creado el 02/07/2014

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Detalles

The discrete mollification method is a data smoothing procedure, based on convolution, that is appropriate for the stabilization of explicit schemes for the numerical solution of partial differential equations and the regularization of ill-posed problems. This text introduces some of the main results and recent developments in discrete mollification and discusses several important topics of current research interest. 

The book develops and applies numerical methods based on discrete mollification for a variety of situations arising in applied mathematics, including convection-diffusion equations, conservation laws, strongly degenerate parabolic equations and several system identification problems. For each topic there are theoretical considerations concerning stability and convergence and a generous amount of illustrative examples. The intended audience for this book includes mathematicians, physicists and engineers. 
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Información adicional

Editor / Marca Universidad Nacional de Colombia
Ciudad Bogotá
Facultad Vicerrectoría General
Año de Edición 2014
Número de Páginas 112
Idioma(s) Español
Terminado Rústica
Alto y ancho 17 x 24 cm.
Peso 0.2200
Tipo Producto libro
Colección Technó
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Carlos Daniel Acosta, Carlos Enrique Mejía

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List of Tables 
List of Figures 
Nomenclature 
Acknowledgements 
Foreword 
Abstract 

Chapter 1 
Overview 

1.1 Discrete Mollification 
1.2 Mollification Weights 
1.3 Consistency, Stability and Convergence 
1.4 Thinking About Nonlinearity 
1.5 Boundary Conditions 
1.5.1 Zero Padding Boundary Condition 
1.5.2 Scaled Boundary Condition 
1.5.3 Periodic Boundary Condition 
1.5.4 Boundary Condition by Reflection 
1.6 Parameter Selection 
1.7 Nonlinear Operator 
1.8 Looking Back 
1.9 Concluding Remarks 

Chapter 2 
Convection dominated diffusive problems 

2.1 The Basic Scheme 
2.2 Two Mollified Explicit Schemes 
2.2.1 Stability 
2.2.2 Consistency 
2.3 Numerical Experiments 
2.4 Concluding Remarks 

Chapter 3 
Conservation laws 

3.1 Mollified Lax-Friedrichs Schemes (MLxF) 
3.1.1 Consistency of Mollified Schemes 
3.1.2 Linear Stability Analysis 
3.2 Mollified Nessyahu-Tadmor (MNT) Schemes 
3.2.1 Methods MNT1 and MNT2 
3.2.2 Method MNT3 
3.3 Numerical Experiments 
3.4 Concluding Remarks 

Chapter 4 
Nonllnear and degenerate diffusive problems 

4.1 Mollified Operator Splitting 
4.1.1 The Diffusion Step 
4.1.2 The Operator Splitting Method 
4.1.3 The Nonlinear Convection-Diffusion Equation 
4.1.4 Implementation 
4.1.5 Numerical Experiments 
4.1.6 Concluding Remarks 
4.2 Strongly Degenerate Parabolic Equations 
4.2.1 The Schemes 
4.2.2 Example: Sedimentation
4.3 Concluding Remarks 

Chapter 5 
System identification 

5.1 A Diffusion Coefficient 
5.1.1 Direct Problem 
5.1.2 Inverse Problem 
5.2 Numerical Algorithms 
5.2.1 Coefficient K(x,u) = 1 +a(x)u2 
5.2.2 CoefficientK(x,u)=a(x)+u2 
5.3 Numerical Experiments 
5.4 Strongly Degenerate Parabolic Equations 
5.5 Para meter Identification 
5.6 Discretization of the Inverse Problem 
5.7 Numerical Experiments 
5.8 Concluding Remarks 

Chapter 6 
Literature review 

6.1 System Identification 
6.1.1 Source Terms in a 1-D IHCP 
6.1.2 Source Terms in a 2-D IHCP 
6.1.3 Parameters in a Transport Equation 
6.1.4 Parameters in a Drying System 
6.2 Fractional Calculus 
6.2.1 Caputo Fractional Derivatives 
6.2.2 Source Term Identification in a TFDE 
6.3 Multiscale Analysis 
6.4 Concluding Remarks 

Bibliography 
Index 

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