Weather Prediction by Numerical Process (Classic Reprint) - Hardcover

Lewis F. Richardson

9780483438613: Weather Prediction by Numerical Process (Classic Reprint)

Hardcover

ISBN 10: 0483438618 ISBN 13: 9780483438613

Publisher: Forgotten Books, 2019

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Excerpt from Weather Prediction by Numerical Process

In Ch. 7 the arrangement of the tabular numbers in space and time is discussed with a view to securing the best representation of differential coefficients by difference ratios.

In Ch. 8 the whole system of arithmetical operations is reviewed in order. With regard to the horizontal differential coefficients the general method may be briefly described in the following four sentences Take the differential equations and replace everywhere the infinitesimal operator a by the finite difference operator 6. Use arith metic instead of symbols. Attend carefully to the centering of the differences. Leave the errors due to the finiteness of the differences over for consideration at the end of the process. With regard to the vertical differential coefficients, on the contrary, it is oft-en possible to effect an exact transformation to differences, by means of a vertical integration. In arranging the computing, it has constantly to be borne in mind that the rate of change with time of every one of the discrete values of the dependent variables must be calculable from their instantaneous distribution in time and space, excepting' only those values near the edge of the horizontal area represented in the table. We may refer to this necessary property by saying, for brevity, that the system must be lattice-reproducing.

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