A Numerical Study for the Dirichlet Problem of the Helmholtz Equation

In this paper, an effective numerical method for the Dirichlet problem connected with Helmholtz equation is proposed. We choose a single-layer potential approach to obtain boundary integral density function, and then we deal weakly singular kernel of via value decomposition Nystrom method. The direct noisy data solved using Tikhonov regularization method, which used filter out errors in condition data, although problems under investigation are well-posed. Finally, few examples provided demonstrate effectiveness proposed including piecewise curves corners.