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<math>\frac{dx_n}{dt}=f_n(t,x_1,x_2,...x_n)</math> | <math>\frac{dx_n}{dt}=f_n(t,x_1,x_2,...x_n)</math> | ||
| − | When the <math>n</math> ODEs are not all linear, this is a nonlinear system of ODE. | + | When the <math>n</math> ODEs are not all linear, this is a nonlinear system of ODE. In this tutorial, we will see nonlinear systems in different aspects to build up a basic completed concept. </font> |
Revision as of 20:19, 20 November 2017
Non-Linear Systems of ODEs
A slecture by Yijia Wen
6.0 Concept
Consider the system of ODEs in 4.0,
$ \frac{dx_1}{dt}=f_1(t,x_1,x_2,...x_n) $
$ \frac{dx_2}{dt}=f_2(t,x_1,x_2,...x_n) $
...
$ \frac{dx_n}{dt}=f_n(t,x_1,x_2,...x_n) $
When the $ n $ ODEs are not all linear, this is a nonlinear system of ODE. In this tutorial, we will see nonlinear systems in different aspects to build up a basic completed concept.
6.1 Non-Linear Autonomous System
6.2 Non-Linear Non-Autonomous System
6.3 Exercises
6.4 References
Institute of Natural and Mathematical Science, Massey University. (2017). 160.204 Differential Equations I: Course materials. Auckland, New Zealand.
Robinson, J. C. (2003). An introduction to ordinary differential equations. New York, NY., USA: Cambridge University Press.
