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Spline Function Approximations for Solutions of Ordinary Differential Equations by Frank R. Loscalzo; Thomas D. Talbot is a Engineering article available to read on EtoBox.

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A procedure for obtaining spline function approximations for solutions of the initial value problem in ordinary differential equations is presented. The pro- posed method with quadratic and cubic splines is shown to be related to the wellknown trapezoidal rule and Milne-Simpson method, respectively. The method is shown to be divergent, however, when higher degree spline functions are used. y f(x, y), about which we make the following assumptions. If T {(x, Y) 0 -< x =< b}, then we assume that f(x, y) C m-in T and that it sutisfies the Lipschitz condition (2) If m 3 then (2) is equivalent to the boundedness of Of/Oy in T. These conditions on f(x, y) guarantee the existence of a unique solution to (1) for any initial couditiom Our constructi()n of the approximate sohtion S(x) S.(x) is as fol-

Who reads Spline Function Approximations for Solutions of Ordinary Differential Equations?

Author

Frank R. Loscalzo; Thomas D. Talbot

Published

1967

Language

EN

Field

Engineering (Physical Sciences)