Glagah Eskacakra Setyowisnu, Nikenasih Binatari
Green's function for Dirichlet Boundary Condition has been considered by numerous researchers. In this paper, we will derive Green's function from homogeneous two-dimensional wave equation with Dirichlet boundary condition by using separation of variables method. The two-dimensional wave equation's solution is defined as a product of functions of each independent variable, so that three ordinary differential equations (ODE) by those independent variables are obtained. Then, a nontrivial solution of ODE can be obtained by applying the Dirichlet boundary condition. According to the superposition principle, a linear combination of every nontrivial solution is the solution of PDE. Meanwhile, the corresponding coefficient of the given initial value can be obtained by applying the property of base function orthogonality. The corresponding Green's function of its initial value is the result of this paper. For illustration, the obtained solution will be shown graphically for a specific initial value. © 2024 Author(s).
Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, Universitas Negeri Yogyakarta, Yogyakarta, Indonesia
