Abstract:

Computational mathematics and numerical simulation have become essential tools for solving complex engineering problems and supporting sustainable infrastructure development. These techniques enable engineers to model, analyze, and optimize systems before physical implementation, reducing cost, time, and material consumption. Numerical methods such as the Finite Element Method (FEM), Finite Difference Method (FDM), and Finite Volume Method (FVM) are widely used in structural analysis, fluid dynamics, heat transfer, and energy systems. Recent advancements in artificial intelligence (AI), digital twins, and high-performance computing have further improved simulation accuracy and decision-making. This review highlights the importance of computational mathematics, major numerical simulation methods, their applications in smart engineering systems, and their contribution to sustainable infrastructure. It also discusses current challenges and future research directions for developing efficient, reliable, and environmentally friendly engineering solutions.