Exploring the Role of Numerical study Analysis in Scientific Computing: A Qualitative Interview

Abstract

This study investigates the role of numerical analysis within scientific computing through a qualitative approach, focusing on its applications, challenges, and potential for refinement. Numerical analysis, a critical element of scientific computing, offers algorithmic solutions for problems where exact answers are often unachievable, particularly in complex fields such as climate science, physics, and engineering. The research collected insights from 15 computational scientists and engineers in India via semi-structured interviews to understand practical applications and challenges in numerical analysis. Thematic analysis revealed key themes: the need for precision and efficiency in algorithms, resource and computational constraints, and the importance of adaptability for varying scientific contexts. Experts identified specific numerical methods, such as finite element methods and Monte Carlo simulations, as core tools due to their adaptability and computational robustness. The findings highlight the importance of improving algorithmic precision, reducing computational costs, and enhancing accessibility to meet modern scientific demands. Recommendations for future research include focusing on adaptable, efficient, and user-friendly numerical tools that can bridge interdisciplinary gaps, enabling more effective applications of scientific computing across diverse fields. This study contributes to the understanding of numerical analysis in scientific computing and offers directions for algorithmis