These proceedings present a curated collection of innovative approaches to tackling challenging problems in applied mathematics. These problems, often marked by instability, inaccuracy, and high computational cost, remain at the forefront of mathematical research due to their difficulty. Addressing this demand, the contributions in this volume offer robust numerical methods designed to improve the accuracy and efficiency of their solutions. The book originates from the Go20 Conference 2023, where established experts and emerging researchers explored cutting-edge methodologies. The discussions captured here situate new advancements within a broader historical and theoretical context, providing a well-rounded perspective on these pressing mathematical challenges. Topics covered include: Ordinary Differential Equations (ODEs) with singularities Multi-dimensional and multi-rate systems of Partial Differential Equations (PDEs) High-index Differential-Algebraic Equations (DAEs) Inverse and optimal control problems This collection is a valuable resource for researchers and practitioners working on these or related topics. It offers comprehensive analyses and practical insights that bridge foundational principles with modern numerical innovations.