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This volume presents a curated collection of contributions from the Go20 Conference on Scientific Computing and Software, held May 20-24, 2024, in Gozo, Malta. Go20 is an exclusive, invitation-only event limited to 20 participants, designed to foster deep exchange among leading experts from academia, industry, and the public sector. With no parallel sessions and 45-minute talks by every attendee, the conference offers an intensive forum for sharing cutting-edge research.

All papers included in this proceedings underwent rigorous peer review. The topics reflect the forefront of scientific computing, emphasizing both theoretical advances and their realization in software-bridging abstract algorithms with practical implementation. Areas of focus include:

• Perturbations and backward error analysis
• Domain decomposition techniques
• Superconvergence of non-stiffly accurate implicit Runge-Kutta methods for index-2 DAEs
• Parallel-in-time spectral deferred correction and collocation methods
• Computational approaches for physiological dysfunctions and clinical medicine
• Parameter estimation for multidimensional stochastic differential equations
• Novel operator-splitting and fractional-step methods for real and complex PDEs

These contributions advance the rapidly evolving field of scientific computing, addressing challenges with profound societal impact-from healthcare and medicine to climate modeling and data-driven decision-making. By highlighting the interplay between theory and software, this book serves as a valuable resource for researchers seeking insight into state-of-the-art methods and their practical applications.

Researchers and practitioners in scientific computing, numerical analysis, and applied mathematics-both academic and non-academic-will find this volume an essential reference for the latest developments in algorithms and software for differential equations and linear systems.