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 const...
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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 coeffi*** the solution procedure,the sought solution is approximated by the Pascal polynomials and their particularsolutions for the PEM and PMPS,*** 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 *** mathematical statements are provided to demonstrate the equivalence of the PEM and PMPS bases as they are both bases of a certain polynomial vector ***,some numerical experiments were conducted to validate the implementation of the PEM and *** results demonstrated that the PEM is more accurate and well-conditioned than the PMPS and the multiple-scale technique is essential in these polynomialmethods.
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