| The Galerkin method for solving Poisson type differential equations (which appears in fluid mechanics, solid mechanics and heat transfer etc. problems) with different type of boundary conditions is presented and discussed. Symbolic software Mathematica is used for computation.; The method consists of (1) determining the trial functions which satisfy the given boundary conditions and (2) the use of Galerkin method to get the approximate solution. This method produces results of consistently high accuracy and has breadth of application as wide as any method of weighted residuals. The proposed method is applied to fluid mechanics and heat transfer problems with homogeneous, convective and mixed boundary conditions. The results obtained are compared with exact solutions when ever possible.; In some of the examples Aitken-Shank transformation is used to improve the results. Some general feature of the method as well as some special tips, for its implementations, are discussed. And also the usefulness of symbolic algebra software in analysis of such kind of problems is demonstrated. |
