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 case when an abscissa in the interpolation formula is coincident with the pole is also considered. An error bound is provided and some numerical examples are given to illustrate the formulae developed.

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.

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