中文摘要：

最近,Fokas提出了一种研究二维边值问题的新的变换方法,该方法为求解凸多边形上的线性椭圆偏微分方程提供了一种有效办法.本文对这一方法的可行性和有效性进行了分析,为Fokas变换方法的使用提供了参考.作为一个示例,讨论了楔形域上修正的Helmholtz方程的边值问题.

英文摘要：

A new transform method for investigating boundary value problems in two dimensions was introduced by Fokas recently, which provides an effective approach to solve the linear elliptic PDEs in convex polygonal. In this paper, the feasibility and effectiveness of this method have been analyzed, which provide a reference for the use of Fok~as transform. As an illustration, the boundary value problem for the modified Helmholtz equation in a wedge domain is discussed.