Approximation and Comparison of Strum-LiouvilleBoundary Condition Equation Using Modal and Non-Modal Analysis

Approximate solutions of a differential equation arealways important since, in general cases, there are not exactmethods to solve nonlinear differential equation. In this paperfirst, we find an exact solution for a considered differentialequation of the Green function problem. Then using modalanalysis method, approximate solutions are obtained bycalculating its eigenvalues and the answer is represented as aninfinite series. Keeping sufficient number if its sentences gives anapproximate answer. On the other hand, in the non-modalanalysis, we use Galerkin method to approximate the answer ofthe differential equation. This method depends on expansionfunctions and can have different solutions, therefore, good guessof expansion function gives better approximation even withrespect to modal based methods. The effectiveness of thismethod isdemonstrated using various problems

Keywords:

Modal expansions , Non-modal expansions , Greenfunction , Eigenvalue , Eigenfunction