Equação da onda unidimensional: modelagem e métodos de resolução

Abstract

This work has an approach of characteristics of the group to solve the Partial Differential Equations, focusing mainly on present an alternative methodology, which consist to variable method substitution any other arbitrary for the purpose of further a solution exploration. The broad application of the undulatory theme we chose to work with the Wave Equation by to possibility the using of this proposal techniques on innumerable different Physics studies and the treatment one-dimensional wave because of the potential using on situations with higher dimensions. From a physical situation proposal, it was possible execute a mathematic working to find the feature equation this way found in most books which deal with the theme and starting from the differential equation. Thus, it was two situations which it can appear: as an homogeneous problem or non-homogeneousproblem. Toachievetheseobjectiveswascarriedoutabibliographicresearch of exploratory type at the beginning was possible realize the one-dimensional wave equation solution on three times: first using the traditional method found on Physics and Differential Equation books to show that the method is simple, but limited; second form using the mathematic theoretical framework acquired during the study and reproduction to prove the efficiency calculus by D’Alambert solution, that is a famous feature equation on this kind of problems; and finally it has used again the replacement of variables to solve the non-homogeneous problem which enabled to strengthen the effectiveness of the proposed method by finding the general solution for the wave equation.