George E. Okecha

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An alternative method to the method proposed in [10] for the numerical evaluation of integrals of the form 1 −1 e iφt f (t)dt, where f (t) has a simple pole in (−1, 1) and φ ∈ R may be large, has been developed. The method is based on a special case of Hermite interpolation polynomial and it is comparatively simpler and entails fewer function evaluations(More)
We give sufficient criteria for the existence of convergence of solutions for a certain class of fourth-order nonlinear differential equations using Lyapunov's second method. A complete Lyapunov function is employed in this work which makes the results to include and improve some existing results in literature. This is an open access article distributed(More)
Of concern in this paper is the numerical solution of Cauchy-type singular integral equations of the first kind at a discrete set of points. A quadrature rule based on Lagrangian interpolation, with the zeros of Jacobi polynomials as nodes, is developed to solve these equations. The problem is reduced to a system of linear algebraic equations. A theoretical(More)
The problem considered is that of evaluating numerically an integral of the form /-1 e"*xf(x) dx, where / has one simple pole in the interval [-1,1). Modified forms of the Lagrangian interpolation formula, taking account of the simple pole are obtained, and form the bases for the numerical quadrature rules obtained. Further modification to deal with the(More)
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