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Over the last few decades, numerical simulation has become a critical tool in addressing scientific and engineering complexities, propelled by advancements in computing technology and computational methods. This Special Issue compiles cutting-edge research on mathematical simulation and computational techniques, emphasizing innovative algorithms and their cross-field applications. The focus is on fostering interdisciplinary collaborations and developing robust computational tools to tackle contemporary challenges. It features original contributions from leading researchers, highlighting innovative methodologies and their impact in solving intricate problems. This compilation aims to disseminate knowledge, foster collaborations, and inspire further research, pushing the boundaries of engineering and scientific exploration.