Can the Runge-Kutta method solve the governing equation in the attached article? the mathematical model is a plate includes both geometric nonlinearity and nonlinear stiffness, which teacher can explain? Are there any similar examples?
The Runge-Kutta method is one method for solving ordinary differential equations. So of course it can be used, once the governing equations have been written as such a system of equations. Of course it is necessary to monitor that the solution also satisfies all the constraints, which imposes constraints on the timestep and may make using other methods, that take into account the constraints, a better choice.
Runge-Kutta methods of various orders are derived based on Taylor Series expansions of various orders. There are explicit or implicit RK methods. The explicit single step methods are used to solve systems of first order IVPs (of non-stiff ODEs). The implicit methods are more suitable for stiff differential equations (due to occurrence of numerical instabilities). There are also explicit or implicit multi-step methods, and semi-implicit methods. [Search references!]
Higher order differential equations are transformed into systems of first order ODEs (IVPs) and the above (implicit / explicit) methods are applied based on the type of the ODEs (stiff / non-stiff). Infact, there are other methods...
Many Thanks!
see
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwi04fCXiYbyAhX8URUIHVmtCu8QFjAAegQIBxAD&url=https%3A%2F%2Fmath.stackexchange.com%2Fquestions%2F2175510%2Fcan-runge-kutta-method-be-used-to-solve-non-linear-differential-equation&usg=AOvVaw0mjzW6CMdoBjqcwJIVTxLP
- Badges
- Science topic