We consider the elastic stress near a hole with corners in an infinite plate under biaxial stress. The elasticity problem is formulated using complex Goursat functions, resulting set of singular integro-differential equations on boundary. boundary integral are solved numerically Chebyshev collocation method which augmented by fractional power term, derived asymptotic analysis corner region, to ...

We present a finite difference method for solving parabolic partial integro-differential equations with possibly singular kernels which arise in option pricing theory when the random evolution of the underlying asset is driven by a Lévy process or, more generally, a time-inhomogeneous jumpdiffusion process. We discuss localization to a finite domain and provide an estimate for the localization ...