Note on the Numerical Solution of Linear Differential Equations with Constant Coefficients | Zendy

R. E. Scraton | Zendy; J. W. Searl | Zendy

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Note on the Numerical Solution of Linear Differential Equations with Constant Coefficients

Author(s) -

R. E. Scraton,

J. W. Searl

Publication year - 1963

Publication title -

the computer journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.319

H-Index - 64

eISSN - 1460-2067

pISSN - 0010-4620

DOI - 10.1093/comjnl/6.2.206

Subject(s) - mathematics , constant (computer programming) , computation , differential equation , interval (graph theory) , notation , function (biology) , runge–kutta methods , mathematical analysis , variety (cybernetics) , algorithm , computer science , combinatorics , arithmetic , statistics , programming language , evolutionary biology , biology

The numerical solution of the differential equation ay" + by'+ cy = f{x) (1) where a, b, c are constants and f(x) is a numerically specified function, can be obtained by a variety of methods. For automatic computation the RungeKutta method is normally used, but this may be unstable. The procedure described below provides an alternative method which has been found satisfactory where the Runge-Kutta method has failed. Suppose that f(x) is tabulated at interval h. In the usual notation, let/,, denote f(x0 + ph) so that equation (1) may be written

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