Stiff Scalar Ordinary Differential Equation

Stiff scalar ordinary differential equations (ODEs) pose significant challenges for numerical solution due to their widely varying timescales. Current research focuses on developing and analyzing novel numerical methods, particularly physics-informed neural networks (PINNs) and their variants, including those incorporating characteristics or reduced-order integration techniques, to efficiently and accurately solve these equations. These approaches aim to improve upon traditional methods by offering enhanced stability, accuracy, and computational efficiency, especially for problems exhibiting complex dynamics or high dimensionality. The improved solution of stiff ODEs has broad implications across scientific disciplines, impacting areas such as chemical kinetics, biological modeling, and the solution of partial differential equations.