Ordinary Differential Equations (ODEs) using power series expansion methods such as Taylor’s series.
Power series method generates solution through:
In Taylor series method for ODEs, the term y(x+h) is computed using:
The truncation error in Taylor series method decreases when:
Power series solutions are typically expanded around:
If only the first derivative term is retained in Taylor expansion, the method becomes equivalent to:
The radius of convergence of a power series solution depends on:
The main advantage of Taylor series method over Euler’s method is:
For nonlinear ODEs, Taylor series method:
Increasing the number of series terms generally:
The graphical output in the simulator is useful to: