Linearization: Difference between revisions

Revision as of 13:53, 17 April 2020

Revision as of 20:07, 16 May 2020

Line 51:

===Stability analysis===

In [[stability theory|stability]] analysis of [[Autonomous_system_(mathematics)|autonomous systems]], one can use the [[eigenvalue]]s of the [[Jacobian matrix and determinant|Jacobian matrix]] evaluated at a [[hyperbolic equilibrium point]] to determine the nature of that equilibrium. This is the content of [[linearization theorem]]. For time-varying systems, the linearization requires additional justification.<ref>{{cite journal |first=G. A. |last=Leonov |first2=N. V. |last2=Kuznetsov |title=Time-Varying Linearization and the Perron effects |journal=[[International Journal of Bifurcation and Chaos]] |volume=17 |issue=4 |year=2007 |pages=1079–1107 |doi=10.1142/S0218127407017732 |bibcode=2007IJBC...17.1079L }}</ref>

===Microeconomics===

Line 60:

===Multiphysics===

In [[multiphysics]] systems—systems involving multiple physical fields that interact with one another—linearization with respect to each of the physical fields may be performed. This linearization of the system with respect to each of the fields results in a linearized monolithic equation system that can be solved using monolithic iterative solution procedures such as the [[Newton-Raphson]] method. Examples of this include [[MRI scanner]] systems which results in a system of electromagnetic, mechanical and acoustic fields.<ref>{{cite journal |first=S. |last=Bagwell |first2=P. D. |last2=Ledger |first3=A. J. |last3=Gil |first4=M. |last4=Mallett |first5=M. |last5=Kruip |year=2017 |title=A linearised ''hp''–finite element framework for acousto-magneto-mechanical coupling in axisymmetric MRI scanners |journal=International Journal for Numerical Methods in Engineering |volume=112 |issue=10 |pages=1323–1352 |doi=10.1002/nme.5559 |bibcode=2017IJNME.112.1323B |doi-access=free }}</ref>

==See also==