numerical solution

简明释义

数值解

英英释义

例句

1.To solve the differential equation, we implemented a numerical solution method.

为了求解微分方程，我们实施了一种数值解方法。

2.We verified the accuracy of our numerical solution by comparing it with analytical results.

我们通过将我们的数值解与解析结果进行比较来验证其准确性。

3.In fluid dynamics, a numerical solution is often required to predict flow behavior.

在流体动力学中，通常需要一个数值解来预测流动行为。

4.The engineers used a numerical solution to analyze the stress distribution in the bridge.

工程师们使用了一个数值解来分析桥梁中的应力分布。

5.The simulation provided a numerical solution that matched the experimental results closely.

该模拟提供了一个与实验结果非常接近的数值解。

作文

In the realm of mathematics and engineering, the concept of a numerical solution (数值解) plays a crucial role in solving complex problems that cannot be addressed through analytical methods. Unlike traditional analytical techniques, which often yield exact solutions, numerical solutions (数值解) provide approximate answers that are sufficiently accurate for practical applications. This distinction is particularly important in fields such as fluid dynamics, structural analysis, and thermodynamics, where the governing equations are often nonlinear and difficult to solve analytically.The process of obtaining a numerical solution (数值解) typically involves discretizing the problem at hand. This means breaking down continuous variables into discrete values that can be easily manipulated by computational algorithms. For instance, when dealing with differential equations, the domain might be divided into a grid or mesh, allowing for the application of various numerical methods such as finite difference, finite element, or spectral methods. Each of these techniques has its own advantages and limitations, making the choice of method critical depending on the specific requirements of the problem.One of the most significant advantages of using numerical solutions (数值解) is their ability to handle complex geometries and boundary conditions that would be nearly impossible to solve analytically. For example, in structural engineering, when analyzing the stress distribution in an irregularly shaped beam, a numerical solution (数值解) can provide insights into how the material will behave under various loading conditions. By employing software tools that implement these numerical methods, engineers can simulate real-world scenarios and optimize designs accordingly.However, it is essential to recognize that numerical solutions (数值解) are not without their challenges. One major concern is the issue of convergence, which refers to whether the numerical method will yield results that approach the true solution as the discretization is refined. If a method does not converge, it may lead to inaccurate results, potentially compromising the integrity of the analysis. Additionally, the computational cost associated with obtaining numerical solutions (数值解) can be significant, particularly for large-scale problems that require extensive resources and time.To mitigate these challenges, researchers and practitioners continuously strive to develop more efficient algorithms and improve existing methods. Advances in computing technology have also played a vital role in enhancing the capabilities of numerical solutions (数值解). With the advent of high-performance computing and parallel processing, it is now possible to tackle larger and more complex problems than ever before.In conclusion, the significance of numerical solutions (数值解) in modern science and engineering cannot be overstated. They provide a powerful tool for tackling problems that defy analytical solutions, enabling professionals to make informed decisions based on realistic simulations. As technology continues to evolve, the accuracy and efficiency of numerical solutions (数值解) will undoubtedly improve, further expanding their applicability across various disciplines. Therefore, understanding and mastering the concept of numerical solutions (数值解) is essential for anyone looking to excel in technical fields that rely heavily on mathematical modeling and simulation.

在数学和工程领域，数值解（numerical solution）的概念在解决无法通过解析方法处理的复杂问题中发挥着至关重要的作用。与传统的解析技术不同，后者通常会产生精确解，数值解（numerical solution）提供了足够准确的近似答案，适用于实际应用。这一区别在流体动力学、结构分析和热力学等领域尤为重要，因为这些领域的控制方程往往是非线性的，难以进行解析求解。获得数值解（numerical solution）的过程通常涉及对所处理问题进行离散化。这意味着将连续变量分解为可以被计算算法轻松操作的离散值。例如，在处理微分方程时，可能会将域划分为网格或网格，从而允许应用各种数值方法，如有限差分法、有限元法或谱方法。每种技术都有其优缺点，因此根据问题的具体要求选择合适的方法至关重要。使用数值解（numerical solution）的一个显著优点是它们能够处理复杂的几何形状和边界条件，而这些条件几乎不可能通过解析方式解决。例如，在结构工程中，当分析不规则形状梁中的应力分布时，数值解（numerical solution）可以提供材料在各种加载条件下的行为见解。通过采用实施这些数值方法的软件工具，工程师可以模拟现实场景，并相应地优化设计。然而，必须认识到，数值解（numerical solution）并非没有挑战。其中一个主要问题是收敛性，即数值方法是否会在离散化精细化时产生接近真实解的结果。如果一种方法不收敛，可能会导致不准确的结果，从而可能危及分析的完整性。此外，获得数值解（numerical solution）所需的计算成本可能很高，特别是对于需要大量资源和时间的大规模问题。为了缓解这些挑战，研究人员和从业者不断努力开发更高效的算法并改善现有方法。计算技术的进步也在增强数值解（numerical solution）能力方面发挥了重要作用。随着高性能计算和并行处理的出现，处理比以往更大和更复杂的问题成为可能。总之，数值解（numerical solution）在现代科学和工程中的重要性不容小觑。它们为处理无法用解析解解决的问题提供了强大的工具，使专业人士能够根据现实模拟做出明智的决策。随着技术的不断发展，数值解（numerical solution）的准确性和效率无疑会提高，进一步扩展其在各个学科中的适用性。因此，理解和掌握数值解（numerical solution）的概念对于希望在依赖数学建模和仿真的技术领域中脱颖而出的人至关重要。