时间分数阶Black-Scholes方程在期权定价中有着日益广泛的应用。本文旨在研究该方程的数值解法，构造和分析了两个有效算法。第一个算法结合了时间方向的有限差分和空间方向的谱方法；第二个方法则基于时空Galerkin谱方法。通过引入恰当的Sobolev空间，我们构建了时空变分问题，证明了时空弱问题的适定性。在算法分析方面，我们首先给出两种方法的最优误差估计。然后讨论算法实现技巧，通过选取适当的基函数导出离散问题的线性系统。最后给出一些数值例子验证理论结果。The time fractional Black-Scholes equation is playing increasingly important role in option pricing nowadays. In this paper we investigate the numerical solution of this equation,and propose and analyze two different methods for it. The first proposed method combines a finite difference scheme in time and spectral method in space; while the second one makes use of spectral approximation in both ti...学位：理学硕士院系专业：数学科学学院_计算数学学号：1902013115266
