MatrixPolynomial_Solving_withMATLAB

在数值线性代数中，雅可比方法是一种迭代算法，用于确定严格对角占优线性方程组的解。该方法通过求解每个对角线元素并插入一个近似值，随后迭代该过程直到收敛。此算法是矩阵对角化雅可比变换方法的精简版。该方法以卡尔·古斯塔夫·雅各比（Carl Gustav Jacobi）的名字命名。

This method can solve various partial differential equations and represents the latest numerical solution techniques. It is based on MATLAB programming, making it easier to understand and implement. By utilizing MATLAB, complex mathematical models become more accessible and the process of solving PD

Matlab 开发 - Newton-Raphson 方法。牛顿-拉斐逊法用于求解多项式的所有实根。该方法通过迭代不断逼近函数的零点，适用于求解非线性方程的根。具体步骤如下： 定义多项式和它的导数。 选择一个初始猜测值（x0）。 使用 Newton-Raphson 迭代公式： x_{n+1} = x_n - f(x_n)/f'(x_n) 重复步骤3直到满足精度要求。 代码示例： function roots = newtonRaphson(f, df, x0, tol, maxIter) x = x0; for i = 1:maxIter x = x -

The HowarthsTransformation.m file provides a framework for solving boundary layer problems using the Howarth's Transformation. The function takes the following parameters: y3y5_0 = HowarthsTransformation(rhofun, miufun, hw, M, Pr, Gamma, y3y5_0guess), with default values:- rhofun = @(h) h^(-1)- miu

This code uses the Newton-Raphson method to calculate the roots of transcendental equations. The method includes enhanced features, such as handling cases where the function's derivative disappears, or when the initial approximation is poor, leading to infinite loops due to the non-existence of the

给定组装质量、刚度矩阵和阻尼矩阵，n个自由度的外部载荷矢量，系统对外部载荷的响应使用Wilson Theta逐步积分法计算。在时间步长上，可以根据问题更改Theta值，以调整数值精度和稳定性。 步骤：1. 输入质量、刚度和阻尼矩阵。2. 设定外部载荷矢量。3. 选择合适的Theta值（通常为0.5、1.0等）。4. 逐步计算系统响应。5. 输出计算结果并进行分析。

The following differential schemes are used to solve the given problem: First Scheme: Combining equations (18), (21), and (22), we derive a differential scheme for solving problem (7). The general form is given as follows:[u^{n+1} = u^n + \Delta t \left( -\left( \frac{d^2 u}{dx^2} \right)^n \right

This code solves the Fokker-Planck equation for the dynamic mass-spring-damper system depicted in the ForceBalance.png, considering only a single 'substrate' interaction. It can be used to validate the numerical simulations of the modified multi-bond model under the condition of a single substrate i