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An application of linear analysis to initial value problems Law, Alan Greenwell

Abstract

Certain properties of an unknown element u in a Hilbert space are investigated. For u satisfying certain linear constraints, it is shown that approximations to u and error bounds for the approximations may be obtained in terms of functional representers. The general approximation method is applied to homogeneous systems of ordinary linear differential equations and various formulae are derived. An Alwac III-E digital computer was used to compute optimal approximations and error bounds with the aid of these formulae. Numerous applications to particular systems are mentioned. On the basis of the numerical results, certain remarks are given as a guide for the numerical application of the method, at least in the framework of ordinary differential equations. From the cases studied it is seen that this can be a practicable method for the numerical solution of differential equations.

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