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- W58987788 abstract "The Deferred Approach to the Limit The editorial of the April issue of Mathematics Today drew attention to the fiftieth anniversary of the death of Lewis Fry Richardson. Richardson (1881–1953), a most original thinker, made significant advances in several branches of mathematics and science. A collection of his scientific papers has been published [1] and a biography of this eccentric and uniquely talented scientist has been written [2]. Modern weather forecasting follows essentially the lines mapped out in his magnum opus Weather Prediction by Numerical Process [3]. The Richardson number recalls his fundamental work on turbulence. He spent some years researching quantitative psychology and made notable contributions to the field. His final years were devoted to ‘peace studies’ and his work is the basis of modern conflict resolution research. In the course of his peace studies, he discovered the scaling properties of curves such as coastlines, inspiring Mandelbrot’s theory of fractals. Most relevant in the current context is Richardson’s introduction of finite difference methods for the solution of partial differential equations. The finite difference method was developed by Richardson in his study of stresses in masonry dams [1]. The derivative dy/dx of a function y(x) exists if the ratio [( ( )) ( )] / y x h y x h + − tends to a definite limit as the increment h tends to zero. Differential calculus depends upon justifying the limiting process h → 0. In approximating a differential equation by finite differences, we reverse the procedure, and replace derivatives by corresponding ratios of increments of the dependent and independent variables. Richardson [4] described the procedure thus:" @default.
- W58987788 created "2016-06-24" @default.
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- W58987788 date "2003-01-01" @default.
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- W58987788 title "Richardson Extrapolation: The Power of the 2-gon" @default.
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