A Unifying Theory for Runge-Kutta-like Time Integrators : Convergence and Stability
by
Thomas Izgin
Book Details
Format
Paperback / Softback
Book Series
Ausgewahlte Kapitel der Angewandten Mathematik, Numerik und des wissenschaftlichen Rechnens
ISBN-10
365851714X
ISBN-13
9783658517144
Publisher
Springer Fachmedien Wiesbaden
Imprint
Springer Spektrum
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Aug 6th, 2026
Print length
189 Pages
Product Classification:
Cybernetics & systems theoryCybernetics and systems theoryNumerical analysis
Ksh 12,600.00
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Many dynamical systems in science and engineering are governed by differential equations whose solutions must remain positive and conservative. Standard numerical methods often fail to preserve these essential properties, leading to unphysical results such as negative concentrations or loss of mass. This book presents a rigorous analytical study of modified Patankar-type schemes, a class of nonlinear time-integration methods that guarantee unconditional positivity and exact conservation while achieving at least second-order accuracy. Beyond this specific class, many of the theoretical results are shown to be applicable to general nonlinear numerical methods, providing broader insight into the design of structure-preserving schemes.
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