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Browsing Staff Publication by Author "A. H. AHMED"

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    COMPUTABLE ERROR BOUNDS FOR COLLOCATION METHODS
    (1995) A. H. AHMED
    This paper deals with error bounds for numerical solutions of linear ordinary differential equations by global or piecewise polynomial collocation methods which are based on consideration of the involved differential operator, related matrices and the residual. It is shown that significant improvement may be obtained if direct bounds for the error in the solution are considered. The practical implementation of the theory is illustrated by a selection of numerical examples.
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    ERROR ESTIMATION FOR COLLOCATION SOLUTION OF LINEAR ORDINARY DIFFERENTIAL EQUATIONS
    (1986) A. H. AHMED; K. WRIGHT
    Al~ract--This paper is concerned with error estimates for the numerical solution of linear ordinary differential equations by global or piecewise polynomial collocation which are based on consideration of the differential operator involved and related matrices and on the residual. It is shown that a significant advantage may be obtained by considering the form of the residual rather than
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    THE RESIDUAL AND THE ERROR FOR COLLOCATION METHODS
    (Hindawi Publishing Corp, 2001) A. H. AHMED
    We use earlier results on collocation matrices related to the solution and its derivatives in describing asymptotic relation between the error on the highest derivative and the residuals. That justifies the use of the form of the residual rather than its norm in measuring the error.