Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations: 1st Edition (Paperback) book cover

Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations

1st Edition

By V. Lakshmikantham, S. Koksal

CRC Press

328 pages

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Paperback: 9780367395407
pub: 2019-09-11
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Hardback: 9780415305280
pub: 2003-02-27
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Description

A monotone iterative technique is used to obtain monotone approximate solutions that converge to the solution of nonlinear problems of partial differential equations of elliptic, parabolic and hyperbolic type. This volume describes that technique, which has played a valuable role in unifying a variety of nonlinear problems, particularly when combined with the quasilinearization method. The first part of this monograph describes the general methodology using the classic approach, while the second part develops the same basic ideas via the variational technique. The text provides a useful and timely reference for applied scientists, engineers and numerical analysts.

Table of Contents

Elliptic Equations. Monotone Iterates: A Preview. Monotone Iterative Technique. Generalized Quasilinearization. Weakly Coupled Mixed Monotone Systems. Elliptic Systems in Unbounded Domains. MIT Systems in Unbounded Domains. Parabolic Equations. Comparision Theorems. Monotone Iterative Technique. Generalized Quasilinearization. Monotone Flows and Mixed Monotone Systems. GCR for Weakly Coupled Systems. Stability and Vector Lyapunov Functions. Impulsive Parabolic Equations. Comparison Results for IPS. Coupled Lower and Upper Solutions. Generalized Quasilinearization. Population Dynamics with Impulses. Hyperbolic Equations. VP and Comparison Results. Monotone Iterative Technique. The Method of Generalized Quasilinearization. Elliptic Equations. Comparison Result. MIT: Semilinear Problems. MIT: Quasilinear Problems. MIT: Degenerate Problems. GQ: Semilinear Problems. GQ: Quasilinear Problem. GQ: Degenerate Problems. Parabolic Equations. Monotone Iterative Technique. Generalized Quasilinearization. Nonlocal Problems. GQ: Nonlocal Problems. Quasilinear Problems. GQ: Quasilinear Problems. Hyperbolic Equations. Notation and Comparison Results. Monotone Iterative Technique. Generalized Quasilinearization. Appendices.

About the Authors

Lakshmikantham, V.; Koksal, S.

About the Series

Mathematical Analysis and Applications

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations
SCI040000
SCIENCE / Mathematical Physics