Growing demand for simulation of scientific and engineering problems requires faster and more accurate numerical solution of partial differential equations (PDEs). In this research, a new approach is proposed, from a new point of view, for the solution of such PDEs. The approach is based on using a linear combination of bases which satisfy the differential equation. The coefficients of these bases are calculated using a method developed by the author such that the boundary conditions are satisfied in a point-wise manner. This approach may be used in the solution of linear PDEs, enabling solution of a Various forms of the proposed approach have been developed to solve different types of problems. In each form, semi-analytic version, using continuous functions and discrete version, using a numerical method like the Finite Element Method (FEM) has been studied. Also, the usage of these forms in problems on domains with homogeneous and periodic material properties is addressed. To this end, first a direct form of the proposed approach has been developed for problems defined on bounded domains. The numerical examples show that the direct form can be used to solve this ltr"
