The use of FourierFourier method series for solving differential equations is often referred to as the Fourier method. The Fourier series is a technique for decomposing complex functions in terms of a series of sinesSine series and cosines, or other closely related types of elementary functions. The application of the Fourier method commonly arises when addressing boundary value problems associated with linear homogeneous partial differential equations. This method, together with the eigenfunction expansion, provides a structured procedure that helps in solving intricate mathematical challenges inherent in various scientific and engineering applications.