Simplify solving differential equations with this MATLAB suite! This paper introduces a comprehensive software suite consisting of 17 MATLAB functions designed to facilitate the spectral collocation (pseudospectral) method for solving differential equations. The suite includes functions for computing derivatives of arbitrary order using Chebyshev, Hermite, Laguerre, Fourier, and sinc interpolants. Auxiliary functions are also included for incorporating boundary conditions, performing interpolation using barycentric formulas, and computing roots of orthogonal polynomials. The capabilities of the package are showcased through applications to eigenvalue, boundary value, and initial value problems arising in special functions, quantum mechanics, nonlinear waves, and hydrodynamic stability. This MATLAB suite provides researchers and engineers with a powerful and user-friendly toolkit for tackling complex differential equations across diverse scientific domains. Its comprehensive set of functions and illustrative examples make it a valuable resource for both experienced users and those new to the spectral collocation method.
As a publication focused on mathematical software, ACM Transactions on Mathematical Software is an ideal venue for this paper. The introduction of a MATLAB suite for solving differential equations directly aligns with the journal's aim of disseminating high-quality, well-documented software tools for mathematical problem-solving. This contribution enhances the accessibility and efficiency of spectral collocation methods for a wide range of applications.