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Browsing Computing & Computer Sciences by Author "A. H. AHMED"
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- ItemCOMPUTABLE ERROR BOUNDS FOR COLLOCATION METHODS(1995) A. H. AHMEDThis 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.
- ItemERROR ESTIMATION FOR COLLOCATION SOLUTION OF LINEAR ORDINARY DIFFERENTIAL EQUATIONS(1986) A. H. AHMED; K. WRIGHTAl~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
- ItemTHE RESIDUAL AND THE ERROR FOR COLLOCATION METHODS(Hindawi Publishing Corp, 2001) A. H. AHMEDWe 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.