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Partitioned rational Runge Kutta for parabolic systems
Author(s) -
Liu Wing Kam,
Belytschko Ted,
Zhang Yi Fei
Publication year - 1984
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620200904
Subject(s) - integrator , runge–kutta methods , simple (philosophy) , nonlinear system , stability (learning theory) , mathematics , numerical integration , computer science , control theory (sociology) , numerical analysis , mathematical analysis , physics , artificial intelligence , computer network , philosophy , control (management) , bandwidth (computing) , epistemology , quantum mechanics , machine learning
A new family of coupled time integration operators of different orders is developed. It permits different time integration operators to be used simultaneously in various regions of the model. This approach has the advantage of applying a very accurate time integrator, such as Runge Kutta method of order two to four, to the local nonlinear region of interest and a simple time integrator, such as the implicit–explicit or mixed time implicit–explicit method of order one, for the remaining region. The computer implementation aspects, stability analysis as well as the numerical evaluations of these new methods are presented. This is another attractive addition to the repertoire of time integration methods.