Ordinary Differential Equations (ODEs) using power series expansion methods such as Taylor’s series.
Power series solution of an ODE assumes the solution in the form:
In Taylor series method for solving ODEs, the next value y(x+h) depends on:
The local truncation error in Taylor series method depends on:
Initial conditions in power series solution are required to:
The accuracy of Taylor series method improves when:
Taylor series expansion is most accurate near:
For the ODE dy/dx = f(x,y), the Taylor series method requires computation of:
If only the first derivative term is used in Taylor expansion, the method reduces to:
The radius of convergence of a power series solution depends on:
Compared to Euler’s method, Taylor series method: