An alternative method to the method proposed in [10] for the numerical evaluation of integrals of the form âˆ« 1 âˆ’1 e iÏ†tf(t)dt, where f(t) has a simple pole in (âˆ’1, 1) and Ï† âˆˆ R may be large, has beenâ€¦ (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^{â€¦ (More)

Abstract Two efficient quadrature formulae have been developed for evaluating numerically certain singular integral equations of the first kind over the finite interval [-1,1]. Central to this workâ€¦ (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, withâ€¦ (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 Lyapunovâ€¦ (More)