The Numerov Process (NP) provides the solution of some classes of ODEs with an accuracy much supe... more The Numerov Process (NP) provides the solution of some classes of ODEs with an accuracy much superior to that of the standard finite-difference or box-integration methods. The original formulation of NP requires a uniform grid, which is a drawback for applications to, e.g., the semiconductor-device equations. Purpose of this work is showing how a method for extending NP to a non-uniform grid is applied to the solution of the drift-diffusion model. The method keeps the fifth-order accuracy of the original NP. In the multi-dimensional case, the variable transformation illustrated in the paper is found beneficial also when standard solution schemes are used; in fact, it makes the current-density vector well defined within each grid element.
The Numerov Process (NP) provides the solution of some classes of ODEs with an accuracy much supe... more The Numerov Process (NP) provides the solution of some classes of ODEs with an accuracy much superior to that of the standard finite-difference or box-integration methods. The original formulation of NP requires a uniform grid, which is a drawback for applications to, e.g., the semiconductor-device equations. Purpose of this work is showing how a method for extending NP to a non-uniform grid is applied to the solution of the drift-diffusion model. The method keeps the fifth-order accuracy of the original NP. In the multi-dimensional case, the variable transformation illustrated in the paper is found beneficial also when standard solution schemes are used; in fact, it makes the current-density vector well defined within each grid element.
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Papers by Massimo Rudan