Soluções de referência para a equação da onda bidimensional

Abstract

The modellin gthrough Differential Equations(DE) has been of great importance for the study of the behavior and comprehension of several phenomena, as well as for the developing of technics for obtaining solutions for these differential equations. The exact solution of a DE is not always possible to be found,and,in this case,the use of numerical methods to obtain approximate solutions is necessary. However, the precision of numerical methods has improved along the years, what makes it difficult to compare them, since the difference in terms of precision of the methods is generally small. In order to provide a support to make comparisons between high precision numerical methods, this work presents two benchmark solutions for two initial value and boundary problems, modeled by the Bidimensional Wave Equation, that includes an adjustment parameter, defi ned as the membrane's frequency of excitation. The parameter, presentin the benchmark solutions, will be used as an arti fice to difficult the approximation of the exact solution, making viable the comparison between highly precise methods. This work also provides the approximation of the solutions of the proposed problem susing the Finite Difference Method, with an analysis about its precisio ntakingin consideration the adjustment parameter.