Wolfram Language

Compute a Series Solution (AsymptoticDSolveValue)

A linear ordinary differential equation can be approximated by a Taylor series expansion near an ordinary point for the equation. This example shows how to obtain such an approximation using AsymptoticDSolveValue.

Compute a Taylor polynomial approximation for the defining ODE of Cos.

Improve the range of the approximation by specifying a higher order.

Study the variation of range with the order of the approximation.

Compute a Taylor approximation for a system of linear ODEs at the ordinary point .

Taylor approximations can often be computed for nonlinear ODEs with analytic coefficients, as illustrated by the following example.

Plot the successive approximations given by the solution.

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