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A Direct Numerov Sixth-order Numerical Scheme to Accurately Solve the Unidimensional Poisson Equation with Dirichlet Boundary Conditions

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Abstract

In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with Dirichlet boundary conditions. Our results should improve numerical codes used mainly in self-consistent calculations in solid state physics.

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Authors and Affiliations

  1. Instituto de Física de São Carlos, Universidade de São Paulo, 13560-970, São Carlos, SP, Brazil

    Esmerindo Bernardes

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  1. Esmerindo Bernardes
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Correspondence to Esmerindo Bernardes.

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Bernardes, E. A Direct Numerov Sixth-order Numerical Scheme to Accurately Solve the Unidimensional Poisson Equation with Dirichlet Boundary Conditions. J Supercond Nov Magn 23, 167–169 (2010). https://doi.org/10.1007/s10948-009-0544-z

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  • DOI: https://doi.org/10.1007/s10948-009-0544-z

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