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.
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.