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The Quarterly Journal of Mechanics and Applied Mathematics 1948 1(1):35-42; doi:10.1093/qjmam/1.1.35
© 1948 by Oxford University Press
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FINITE DIFFERENCE FORMULAE FOR THE SQUARE LATTICE

W. G. BICKLEY

( Imperial College London )

The paper gives approximate formulae for derivatives (including combinations like {triangledown}2 and {triangledown}4), and integrals, of a function of two independent variables, in terms of its values at nodes of a square lattice, primarily for use in the numerical solution of partial differential equations. Consideration is given to the form, as well as to the magnitude, of the leading terms in the error, and what is believed to be for most purposes optimum combinations are thus selected for the simpler compact sets of nodes.


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