This paper provides the theoretical validation of the unconditional stability, using the Von Neumann method, for the radial point interpolation method (RPIM) and Crank-Nicolson (CN) scheme, in a three dimensional (3D) problem. Moreover, the matrix inversion process, typical of the CN implicit scheme, is circumvented and approximated by a finite series for a particular stability factor range. To validate numerically the efficiency of the CN-RPIM unconditional stability, the resonant frequency inside a 2D double ridged rectangular cavity is simulated. The numerical results confirm that the CN-RPIM is significantly efficient, since the simulation time is reduced by up to 90%, and the memory requirement is saved up to 81%, with a few loss of accuracy.
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