A comparative study on polynomial expansion method and polynomial method of particular solutions
摘要：
In this study the polynomial expansion method(PEM) and the polynomial method of particular solutions(PMPS)are applied to solve a class of linear elliptic partial differential equations(PDEs)in two dimensions with constant coefficients. In the solution procedure,the sought solution is approximated by the Pascal polynomials and their particular solutions for the PEM and PMPS, respectively. The multiple-scale technique is applied to improve the conditioning of the resulted linear equations and the accuracy of numerical results for both of the PEM and PMPS. Some mathematical statements are provided to demonstrate the equivalence of the PEM and PMPS bases as they are bases of a certain polynomial vector space. Then, some numerical Numerical results demonstrated that the PEM is more accurate and well-conditioned than the PMPS and the multiple-scale technique is essential in these polynomial meth-ods.
