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With the latest trend in technology the size of the electronic devices has been encountered from the room size computer to nano-scale which has lead to quantum effect. At the length of the nano-scale electrons can only be observed as a wave rather than the particle. According to numerical point of view it is necessary to use a quantum model to analyse these quantum effects. Various researchers have proposed different numerical approaches to observe the quantum effects, for example, upwind difference scheme (UDS), Central difference scheme (CDS), Finite element method (FEM) and Finite volume...