Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations
Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations by V. Lakshmikantham is a comprehensive volume published by CRC Press LLC on September 11, 2019. This 328-page book presents a monotone iterative technique designed to obtain monotone approximate solutions that converge to solutions of nonlinear problems in partial differential equations, specifically those of elliptic, parabolic, and hyperbolic types.
Readers will find a detailed exploration of the methodology behind this technique, which serves to unify various nonlinear problems, particularly when paired with the quasilinearization method. The text is divided into two parts: the first outlines the classic approach to the general methodology, while the second develops these concepts through a variational technique. This work is intended as a valuable reference for applied scientists, engineers, and numerical analysts engaged in the fields of mathematics and physics.
Official synopsis Publisher
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.
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