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The Resource Differential Equations and Numerical Analysis : Tiruchirappalli, India, January 2015

Differential Equations and Numerical Analysis : Tiruchirappalli, India, January 2015

Label
Differential Equations and Numerical Analysis : Tiruchirappalli, India, January 2015
Title
Differential Equations and Numerical Analysis
Title remainder
Tiruchirappalli, India, January 2015
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Contributor
Subject
Language
eng
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Cataloging source
MiAaPQ
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Springer Proceedings in Mathematics and Statistics Ser.
Series volume
v.172
Differential Equations and Numerical Analysis : Tiruchirappalli, India, January 2015
Label
Differential Equations and Numerical Analysis : Tiruchirappalli, India, January 2015
Link
http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=4648530
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Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Preface -- Contents -- Editors and Contributors -- Part I Invited Papers -- Elementary Tutorial on Numerical Methods for Singular Perturbation Problems -- 1 Introduction to Singular Perturbation Problems and Their Numerical Solution -- 2 Fitted Operator Methods -- 3 Fitted Mesh Methods -- 4 Computations -- References -- Interior Layers in Singularly Perturbed Problems -- 1 Introduction -- 2 Linear Singularly Perturbed Problems with Smooth Data -- 3 Singularly Perturbed Initial Value Problems with Discontinuous Data -- 4 Singularly Perturbed Boundary Value Problems with Non-smooth Data -- 5 Singularly Perturbed Turning Point Problems -- 6 Singularly Perturbed Parabolic Problems -- 7 Singularly Perturbed Nonlinear Problems with Interior Layers -- References -- Singularly Perturbed Delay Differential Equations and Numerical Methods -- 1 Introduction -- 2 Preliminaries -- 2.1 Properties of FDE -- 2.2 Classification of FDEs -- 2.3 Method of Steps/Step by Step Integration -- 2.4 Existence, Uniqueness and Stability -- 3 Euler Method for Delay Differential Equations -- 4 Singular Perturbation Problems -- 4.1 One-Dimension Convection Diffusion Problems -- 4.2 Reaction Diffusion Problems -- 5 Locations of Boundary Layers -- 6 Numerical Methods for SPPs -- 6.1 Fitted Mesh Method for Second Order SPDEs 4 -- 7 Numerical Method for Singularly Perturbed Delay Differential Equations (SPPDDs) of First Order -- 8 Location of Boundary Layers for Second Order SPPDDs -- 9 Numerical Methods for Singularly Perturbed Second Order Delay Differential Equations -- 9.1 Initial Value Technique 23 -- 9.2 Asymptotic Numerical Method 24 -- 9.3 An Iterative Numerical Method 27 -- References -- Initial or Boundary Value Problems for Systems of Singularly Perturbed Differential Equations and Their Solution Profile -- 1 Introduction
  • 2 A System of First Order Ordinary Differential Equations -- 2.1 Analytical Results -- 2.2 Shishkin Mesh -- 2.3 Discrete Problem -- 2.4 Discontinuous Source Terms -- 3 System of Second Order Differential Equations of Reaction---Diffusion Type -- 4 Systems of Singularly Perturbed Time Dependent Equations of Reaction-Diffusion Type -- References -- Part II Contributed Papers -- Convergence of the Crank-Nicolson Method for a Singularly Perturbed Parabolic Reaction-Diffusion System -- 1 Introduction -- 2 Analytical Estimates of the Exact Solution -- 3 Crank-Nicolson Semi-discretization in Time -- 4 The Complete Discretisation in Time and Space -- 5 Error Estimate -- 6 Numerical Illustrations -- References -- A Numerical Method for a System of Singularly Perturbed Differential Equations of Reaction-Diffusion Type with Negative Shift -- 1 Introduction -- 2 Maximum Principle and Stability Result -- 3 Iterative Method -- 3.1 Procedure -- 3.2 Convergence Analysis -- 4 Layer Adapted Meshes -- 4.1 Shishkin Mesh -- 4.2 BS Mesh -- 5 First Order Finite Difference Scheme -- 5.1 Scheme -- 5.2 Error Estimate -- 6 Finite Element Method -- 6.1 Scheme -- 6.2 Error Estimate -- 7 Numerical Experiments -- 8 Discussion -- References -- Numerical Method for a Singularly Perturbed Boundary Value Problem for a Linear Parabolic Second Order Delay Differential Equation -- 1 Introduction -- 2 The Continuous Problem -- 3 Analytical Results -- 4 Improved Estimates -- 5 The Shishkin Mesh -- 6 The Discrete Problem -- 7 Error Estimate -- 8 Numerical Illustration -- References -- A Parameter Uniform Numerical Method for an Initial Value Problem for a System of Singularly Perturbed Delay Differential Equations with Discontinuous Source Terms -- 1 Introduction -- 2 Analytical Results -- 3 Shishkin Mesh -- 4 The Discrete Problem -- 5 Error Analysis -- 6 Numerical Illustration
  • References -- A Parameter-Uniform First Order Convergent Numerical Method for a Semi-linear System of Singularly Perturbed Second Order Delay Differential Equations -- 1 Introduction -- 2 Analytical Results -- 3 The Shishkin Mesh -- 4 The Discrete Problem -- 5 Numerical Illustration -- References
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{'f': 'http://opac.lib.rpi.edu/record=b4392753'}
Extent
1 online resource (172 pages)
Form of item
online
Isbn
9788132235989
Media category
computer
Media MARC source
rdamedia
Media type code
c
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Specific material designation
remote

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