By means of the quadrature rules of computing singular periodic functions, mechanical quadrature methods for solving boundary integral equations of plane elasticty problems are presented, which possess high accuracies and low computing complexities. Moreover, the asymptotic expansions with the odd powers of the errors are shown, so that we not only can improve the accuracy order of the approximations by Richardson extrapolation but also can estimate the errors of the approximations by a posteriori error estimations.
本文利用Lalplace变换方法得到带连续红利的美式石看涨期权价格的积分表示,以及最优执行边界满足的一个非线性的第二类Volterra积分方程。然后用数值积分公式给出了积分方程的数值觯,从而得到了带连续红利的美式看涨期权价格及其执行边界的数值解。<正>In this paper, we apply Laplace transform to obtain an integral representation for the solution for American call options with continuous dividend, and get a nonlinear Volterra integral equation of the second kind for the optimal exercise boundary. Then we give the numerical solution to the integral equation using the quadrature formulae, and so get the numerical solution of the price of American call option with continuous dividend and the optimal exercise boundary.
