Implementasi Fast Fourier Transform dalam Penyelesaian Persamaan Difusi Panas Satu Dimensi

The Fast Fourier Transform (FFT) method for solving the 1-D heat diffusion equation offers an efficient approach for resolving partial differential equations (PDEs) with various time steps . FFT is used to transform the 1-D heat diffusion equation into the frequency domain and back to the time domain through inverse FFT. Using mathematical modeling with initial and Dirichlet boundary conditions, the numerical solutions produced by FFT are compared with analytical solutions. The accuracy of the method is validated using MAE and MSE calculated in Matlab. At several time intervals , the obtained MAE and MSE values indicate a good agreement between the numerical and analytical solutions, with very small errors. Numerical stability analysis confirms the reliability of the FFT method across various The variation in time step has a significant impact on the accuracy and stability of the solution. Smaller time steps improve accuracy and stability but require longer computation times. The optimal time step selected in this study is Increasing the number of discretization points also enhances accuracy but implies an increase in computational load and memory usage. The FFT method demonstrates good numerical consistency with increasing