{'fraction_non_alphanumeric': 0.0136986301369863, 'fraction_numerical': 0.0013698630136986301, 'mean_word_length': 5.194915254237288, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Numerical solution of a two-dimensional Helmholtz equation with Dirichlet boundary conditions

Abstract In this paper, we used numerical Methods to find approximate solution for the 2D Helemholtz equation together with Dirichlet boundary conditions. We have applied three methods in specific of getting the numerical solution of this equation. The first method is the finite difference method by five point, the second method is the finite difference method by nine point and the third method it is the finite elements method of the Helmholtz equation. In the regular shape, the enforcement of the solutions is done utilizing spreadsheet. Also, we compared with the numerical solutions it was obtained through these third methods.