Abstract
Several meshless methods that are used to solve the partial differential equations are particular solutions based numerical methods. These numerical methods can only be applied to solve the partial differential equations if researchers have derived a particular solution of some equations beforehand. The main contribution of this article is the derivation of the family of particular solutions of the Poisson’s equation in 3D with the oscillatory radial basis functions in the forcing term. Numerical results obtained by solving three elliptic partial differential equations presented here validates the derived particular solutions in the method of particular solutions.
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