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 iφtf(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 and(More)
By expanding a component of the non-oscillatory part of the integrand in a series of Laguerre polynomials the numerical approximation of integrals of the type $$\mathop \smallint \limits_0^\infty e^{ - \alpha x^2 } f(x^2 ) \cos (bx) dx$$ is obtained. A method to obtain the optimum value for a scaling parameter is provided. Zur numerischen Approximation von(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)
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)
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)
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