
06124903
j
2013a.00716
Prentice, J. S. C.
Relative and absolute error control in a finitedifference method solution of Poisson's equation.
Int. J. Math. Educ. Sci. Technol. 43, No. 5, 684694 (2012).
2012
Taylor \& Francis, Abingdon, Oxfordshire
EN
I75
N45
Poisson's equation
partial differential equations
finitedifference methods
error control
relative error
absolute error
doi:10.1080/0020739X.2011.622800
Summary: An algorithm for error control (absolute and relative) in the fivepoint finitedifference method applied to Poisson's equation is described. The algorithm is based on discretization of the domain of the problem by means of three rectilinear grids, each of different resolution. We discuss some hardware limitations associated with the algorithm, which are mainly due to its secondorder nature. A generalization of the algorithm for finitedifference methods of arbitrary order is presented. We believe that the algorithm is a valuable addition to typical textbook discussions of the fivepoint finitedifference method for Poisson's equation.