Application Research Based on Finite Difference Algorithm

This paper discusses the importance of finite difference algorithms in the field of science and engineering and focuses on methods for both optimization of algorithm efficiency and numerical stability improvement. For algorithm efficiency, optimization methods such as parallel computing techniques, optimized mesh partitioning, selection of appropriate difference formats, adaptive mesh methods, use of high-performance computing platforms, and pre-processing and post-processing techniques are introduced. And for numerical stability, methods to improve the numerical stability of the algorithm are discussed. Through these optimization and improvement methods, the finite difference algorithm can respond to the challenges of complex problems more efficiently and reliably, and provide a more reliable and efficient numerical computation method for scientific research and engineering practice.