BLOCK IMPLICIT ONE-STEP METHOD FOR THE NUMERICAL INTEGRATION OF INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS (Published)
In this paper, block implicit one-step method of order seven is proposed for the numerical integration of first order initial value problems. The method is based on collocation of the differential system and interpolation of the approximate at the grid and off-grid points. The procedure yields six consistent finite difference schemes which are combined as simultaneous numerical integrators to form block method. The method is found to be zero-stable hence convergent. The accuracy of the method is tested with some standard first order initial value problems. The results show a better performance over the existing methods
Keywords: Block, Finite Differential Schemes, Implicit, Simultaneous Numerical Integrators, Zero-Stable And Convergent.
A TECHNIQUE FOR N2¬K FACTORIAL DESIGNS (Published)
This article developed an appealing technique for n2k factorial designs that would generate more compact and more efficient computational results on n2k complete experiments that would be of immense benefit to students and researchers.
The article leveraged on existing body of knowledge on 2k factorial designs to contrive and exploit a series of orthogonal and block diagonal matrices, which formed the basis for the statements and proofs of envisaged results on complete n2k experiments.
The research effort culminated into statements and proofs of what the researcher referred to as Ukwu’s theorem and its corollary. These would elucidate the design process, offer computational advantages on the prosecution of complete n2k experiments, as well as enhance their mathematical appreciation. The utility and applicability of the results of the investigation should be multi-disciplinary in nature and scope.
Keywords: Block, Designs, Effects, Estimated, Factorial, Orthogonal