The Legendre differential equation may be solved using the standard power series method.
2.
It can capture the actual stress values better than the power series method.
3.
The power series method is very stable but it cannot capture rapidly changing stress values.
4.
The power series method can be applied to certain nonlinear differential equations, though with less flexibility.
5.
The Parker Sochacki method is done before the power series method to make the power series method possible on many nonlinear problems.
6.
The Parker Sochacki method is done before the power series method to make the power series method possible on many nonlinear problems.
7.
An ODE problem can be expanded with the auxiliary variables which make the power series method trivial for an equivalent, larger system.
8.
"The power series method " and " the spline method " are other modifications of the integral method.
9.
Since the Parker Sochacki method involves an expansion of the original system of ordinary differential equations through auxiliary equations, it is not simply referred to as the power series method.
10.
Many times, without using auxiliary variables, there is no known way to get the power series for the solution to a system, hence the power series method alone is difficult to apply to most nonlinear equations.
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