摘 要
本文概述了数值分析的基础知识及其在工程领域中的重要应用与发展趋势。数值分析作为研究利用计算机求解数学问题的科学，其基本含义、计算方法和在工程中的意义被详细阐述。在解决工程实际问题方面，数值分析展现了广泛的应用潜力，包括结构分析和优化设计、流体力学模拟以及热传导和温度场分析等关键领域。这些应用不仅提高了工程设计的精度和效率，还推动了相关技术的创新与发展。随着科技的进步，数值分析在工程实践中呈现出新的发展趋势，如高性能计算与云计算的广泛应用，为大规模复杂问题的求解提供了有力支持；同时，人工智能与机器学习的融合也为数值分析带来了新的算法和工具，增强了其解决问题的能力和适应性。此外，多学科交叉与融合也成为数值分析发展的重要方向，推动了工程技术的综合创新和进步。
关键词：数值分析；工程实际问题；应用
Abstract
This paper summarizes the basic knowledge of numerical analysis and its important applications and development trends in the field of engineering. As a science for the study of solving mathematical problems by computer, its basic meaning, computational method and significance in engineering are expounded in detail. In solving practical engineering problems, numerical analysis shows a wide range of applications, including structural analysis and optimization design, fluid mechanics simulation, and thermal conduction and temperature field analysis. These applications not only improve the accuracy and efficiency of engineering design, but also promote the innovation and development of related technologies. With the progress of science and technology, numerical analysis presents a new development trend in engineering practice, such as the wide application of high performance computing and cloud computing, which provides strong support for the solution of large-scale complex problems. Meanwhile, the integration of artificial intelligence and machine learning also brings new algorithms and tools for numerical analysis, enhancing its problem solving ability and adaptability. In addition, multidisciplinary intersection and integration has also become an important direction of the development of numerical analysis, promoting the comprehensive innovation and progress of engineering technology.
Keywords: Numerical analysis; engineering practical problems; applications
目 录
1 引言 1
2 数值分析基础知识概述 1
2.1 数值分析的基本含义 1
2.2 数值计算的基本方法 2
2.3 数值分析在工程领域的重要性 2
3 数值分析在解决工程实际问题中的应用 3
3.1 结构分析和优化设计 3
3.2 流体力学模拟 3
3.3 热传导和温度场分析 4
4 数值分析在工程实践中的发展趋势 4
4.1 高性能计算与云计算的应用 4
4.2 人工智能与机器学习的融合 5
4.3 多学科交叉与融合 5
5 结论 6
致 谢 7
参考文献 8
本文概述了数值分析的基础知识及其在工程领域中的重要应用与发展趋势。数值分析作为研究利用计算机求解数学问题的科学，其基本含义、计算方法和在工程中的意义被详细阐述。在解决工程实际问题方面，数值分析展现了广泛的应用潜力，包括结构分析和优化设计、流体力学模拟以及热传导和温度场分析等关键领域。这些应用不仅提高了工程设计的精度和效率，还推动了相关技术的创新与发展。随着科技的进步，数值分析在工程实践中呈现出新的发展趋势，如高性能计算与云计算的广泛应用，为大规模复杂问题的求解提供了有力支持；同时，人工智能与机器学习的融合也为数值分析带来了新的算法和工具，增强了其解决问题的能力和适应性。此外，多学科交叉与融合也成为数值分析发展的重要方向，推动了工程技术的综合创新和进步。
关键词：数值分析；工程实际问题；应用
Abstract
This paper summarizes the basic knowledge of numerical analysis and its important applications and development trends in the field of engineering. As a science for the study of solving mathematical problems by computer, its basic meaning, computational method and significance in engineering are expounded in detail. In solving practical engineering problems, numerical analysis shows a wide range of applications, including structural analysis and optimization design, fluid mechanics simulation, and thermal conduction and temperature field analysis. These applications not only improve the accuracy and efficiency of engineering design, but also promote the innovation and development of related technologies. With the progress of science and technology, numerical analysis presents a new development trend in engineering practice, such as the wide application of high performance computing and cloud computing, which provides strong support for the solution of large-scale complex problems. Meanwhile, the integration of artificial intelligence and machine learning also brings new algorithms and tools for numerical analysis, enhancing its problem solving ability and adaptability. In addition, multidisciplinary intersection and integration has also become an important direction of the development of numerical analysis, promoting the comprehensive innovation and progress of engineering technology.
Keywords: Numerical analysis; engineering practical problems; applications
目 录
1 引言 1
2 数值分析基础知识概述 1
2.1 数值分析的基本含义 1
2.2 数值计算的基本方法 2
2.3 数值分析在工程领域的重要性 2
3 数值分析在解决工程实际问题中的应用 3
3.1 结构分析和优化设计 3
3.2 流体力学模拟 3
3.3 热传导和温度场分析 4
4 数值分析在工程实践中的发展趋势 4
4.1 高性能计算与云计算的应用 4
4.2 人工智能与机器学习的融合 5
4.3 多学科交叉与融合 5
5 结论 6
致 谢 7
参考文献 8
