Based on the elastodynamic responses of stress [[sigma].sub.ij] (i, j = 1, 2, 3) and displacement [u.sub.i] (i=1, 2, 3), which are obtained using the technique of explicit time integration in FE analysis of the cracked body, the dynamic J-integral (denoted as [J.sup.d]) is calculated as a post-processor by a volume integral, which is derived from a

contour integral applying the divergence theorem, and the virtual crack extension method.

Symbol [H.sup.m,n.sub.p,q](x) stands for well known Fox H-function [11], in operator (4) and (5) defined in terms of Mellin-Barnes type

contour integral as follows:

This paper studies the numerical

contour integral methods (NCIMs) for solving free-boundary partial differential equations (PDEs) from American volatility options written on the volatility whose price follows four well-known models: GBMP, MRGP, MRSRP, and MRLP.

In this paper, we propose a novel and general method to study the local asymptotic stability of positive equilibrium of system (1) by the

contour integral method.

Each contour provides an evaluation of the

contour integral. The number of possible evaluations is the number of such rings of elements.

The quarter of that surface limited by the cone (Figure 6(a)) was calculated by means of the

contour integral [[integral].sub.L] y(x, z)dL.

The relatively less restrictive representation of the fractional derivative according to parameters appears to be the one based on the Pochhammer's

contour integral introduced by Tremblay [31, 32].

We find a simple

contour integral representations for the normalized Schur polynomials (1), (2) with k = 1, i.e.

[q.sub.D](s) can be resumed as the

contour integralA

Contour Integral Involving Fox's H-Function, Indian J.

We may break the

contour integral into two parts and use Eq.

Higgins, Sampling theorems and the

contour integral method, Appl.