The Existence of Fourier Coefficients and Periodic Multiplicity Based on Initial Values and One-Dimensional Wave Limits Requirements - Jufriansah, Adi; Khusnani, Azmi; Hermanto, Arief; Toifur, Mohammad; Prasetyo, Erwin (Jurnal Penelitian Fisika dan Aplikasinya (JPFA), 2020)
Physical systems in partial differential equations can be interpreted in a visual form using a wave simulation. In particular, the interpretation of the differential equations used is in the nonlinear hyperbolic model, but in its completion, there are some limitations to the stability requirements found. The aim of this study is to investigate the analytical and numerical analysis of a wave equation with a similar unit and fractal intervals using the Fourier coefficient. The method in this research is to use the analytical solution approach, the spectral method, and the finite difference method. The hyperbolic wave equation's analytical solution approach, illustrated in the Fourier analysis, uses a pulse triangle. The spectral method minimizes errors when there is the addition of the same sample grid points or the periodic domain's expansion with a trigonometric basis. Meanwhile, different ways offer a more efficient solution. Based on the research results, the information obtained is that the Fourier analysis illustrates the pulse triangle use to solve the solution. These results are also suitable for adding sample points to the same spectra. Fourier analysis requires a relatively long time to solve one pulse triangle graph to need another solution, namely the finite difference method. However, its use is still limited in terms of stability when faced with more complex problems.