Solve a Regular Perturbation OΔE Problem (AsymptoticRSolveValue)

A difference equation depending on a continuous parameter can be solved using a perturbation expansion in terms of the parameter. This example shows how to obtain such an expansion for a regular perturbation problem where the equation can be solved exactly for .

Find an asymptotic expansion for a perturbation problem.

Plot the solution for different values of the parameter.

Compare the value of the perturbation solution with the numerically computed exact solution at . For small values of the parameter , there is excellent agreement, but for larger values (above roughly 0.086), the perturbation solution misses the long-term blowup of the exact solution.