numerical simulation

本程序介绍了应用最为广泛的椭圆型、双曲型、抛物型偏微分方程的数值解法，并详细编程实现了每种方程的多种常见数值解法。附件中使用MATLAB编程来实现这些算法。

本书提供了用Matlab进行数值计算的丰富资料，内容可读性、知识性和实用性都非常强。

数值方法(MATLAB版)(第四版)中文版.pdf

3.2 Genetic Operators (1) Crossover Operator The crossover operator randomly pairs individuals from the parent population for crossover operations, generating ( m ) offspring individuals to form the next generation. Two types of crossover are employed: single-point crossover and two-point crossover. Given two individuals for crossover ( P = {p_1, p_2, p_3, \dots, p_n} ) and ( Q = {q_1, q_2, q_3, \dots, q_n} ), a random crossover point ( b_1 ) is chosen from the range [1, n] for single-point crossover. The elements before ( b_1 ) in ( P ) are copied to offspring individual ( \text{new Individual1} ), while the remaining elements are copied from ( Q ). Similarly, a second offspring ( \text{new Individual2} ) is generated by swapping the roles of ( P ) and ( Q ). In two-point crossover, two random crossover points ( b_1 ) and ( b_2 ) are chosen, and the elements between ( b_1 ) and ( b_2 ) in ( P ) are copied to the offspring, with the remaining elements taken from ( Q ). (2) Mutation Operator After the crossover operation, two mutation operators are applied to the offspring individuals. The first is rotation mutation, where a random position ( \text{bit} ) is chosen, and with probability ( p_m1 ), the portion of the individual after ( \text{bit} ) is rotated. The second is position mutation, with a smaller probability ( p_m2 ), two integers ( \text{bit1} ) and ( \text{bit2} ) are randomly chosen from the range [1, n], and the corresponding parts of the individual are swapped. (3) Selection Operator The fitness of the mutated offspring individuals is evaluated using the lowest level line method. The parent and offspring individuals are ranked by their fitness in descending order, and the top ( m ) individuals are selected as the next generation's parents. 3.3 Termination Criteria The steps in sections 3.2(1), 3.2(2), and 3.2(3) are repeated until the fitness of the best solution meets the required threshold or the pre-defined number of generations is reached. At this point, the optimal solution is output. 4. Case Study To test the performance of the algorithm, two cases from literature [3] are solved. In Case 1, a large rectangle of size ( 15 \times 40 ) is divided into 25 smaller rectangles. Based on the lowest level line method, the corresponding coding sequence is ( \text{Opt} = {1, -9, 11, -15, 17, -24, -25, -10, -14, -22, -23, -2, -3, -5, 18, 7, -8, -12, 19, -20, 21, 6, 13, 4} ). The width is set at 40, and height considerations follow suit for the genetic algorithm implementation.

目前的脚本近似于原始和相关联的对偶（伴随）布拉修斯方程，如Kuehl等人[~11/2020]在关于“连续伴随补充到布拉修斯方程”中的研究所述。数值边值问题使用射击方法近似，其中要解决的初值问题采用4阶Runge-Kutta方法(RK4)。

光纤布拉格光栅 (FBG) 相关的 MATLAB 仿真编程，涉及 信号处理、光纤传输和 光学特性 的模拟与分析。

Simulink 建模和 仿真. Simulink 是一个用于建模、仿真和分析动态系统的工具。该文档为用户提供了 Simulink 的基本操作和高级功能的概述，帮助用户深入理解其应用。

您想要轻松获取科学计算的最新方法吗？这本大幅扩展的第三版《Numerical Recipes》拥有比以往更广泛的覆盖范围，许多新的、扩展的和更新的章节，以及两个全新的章节。采用面向科学应用特别适合的面向对象风格的C++代码，现在采用彩色印刷，便于阅读。《Numerical Recipes》由四位来自学术界和工业界的领先科学家共同撰写，从基本数学和计算机科学开始，逐步演进到完整的工作例程。整本书采用了让早期版本如此受欢迎的非正式、易于阅读的风格。新材料的亮点包括：关于分类和推断的新章节，高斯混合模型，HMMs，层次聚类和SVMs；关于计算几何的新章节，涵盖KD树，四叉树和八叉树，Delaunay三角剖分，以及线段、多边形、三角形和球体的算法。

ContentsPreface to the Second Edition xiPreface to the First Edition xivLicense Information xviComputer Programs by Chapter and Section xix 1 Preliminaries1.0 Introduction 11.1 Program Organization and Control Structures 51.2 Some C Conventions for Scientific Computing 151.3 Error, Accuracy, and Stability 28 2 Solution of Linear Algebraic Equations2.0 Introduction 322.1 Gauss-Jordan Elimination 362.2 Gaussian Elimination with Backsubstitution 412.3 LU Decomposition and Its Applications 432.4 Tridiagonal and Band Diagonal Systems of Equations 502.5 Iterative Improvement of a Solution to Linear Equations 552.6 Singular Value Decomposition 592.7 Sparse Linear Systems 712.8 Vandermonde Matrices and Toeplitz Matrices 902.9 Cholesky Decomposition 962.10 QR Decomposition 982.11 Is Matrix Inversion an (N^3) Process? 102 3 Interpolation and Extrapolation3.0 Introduction 1053.1 Polynomial Interpolation and Extrapolation 1083.2 Rational Function Interpolation and Extr…

在Volterra的封闭系统中，人口增长模型的无量纲形式为 k(du/dt) = u - u^2 - u ∫_0^t u(x) dx。该GUI允许用户输入初始总体 u0、无量纲常数 k、最终时间 Tmax 和网格点数 M。通过单击适当的按钮，用户可以使用各种数值方法生成图。 \"毒性项\" 是积分 ∫_0^t u(x) dx。面板“毒性术语的梯形规则”和“毒性术语的辛普森规则”首先对毒性术语应用正交规则，然后使用指定的数值方法求解所得系统。有关更多信息，请参阅 (1)。有关问题的全面分析，请参阅： 1. Kevin G. TeBeest，Volterra*人口模型的数值和解析解，SIAM Rev. 39 (1997)，第1期。3, 484-493。 2. RD Small，《封闭系统中的人口增长》，SIAM评论25（1983），第1期。1, 93-95。