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首页> 外文期刊>Abstract and applied analysis >A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain
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A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain

机译：基于伯努利运算矩阵的配置方法求解矩形域中的高阶线性复微分方程

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摘要

This paper contributes a new matrix method for the solution of high-order linear complex differential equations with variable coefficients in rectangular domains under the considered initial conditions. On the basis of the presented approach, the matrix forms of the Bernoulli polynomials and their derivatives are constructed, and then by substituting the collocation points into the matrix forms, the fundamental matrix equation is formed. This matrix equation corresponds to a system of linear algebraic equations. By solving this system, the unknown Bernoulli coefficients are determined and thus the approximate solutions are obtained. Also, an error analysis based on the use of the Bernoulli polynomials is provided under several mild conditions. To illustrate the efficiency of our method, some numerical examples are given.
机译：本文为考虑初始条件的矩形域中变系数高阶线性复微分方程的求解提供了一种新的矩阵方法。在提出的方法的基础上，构造了伯努利多项式及其导数的矩阵形式，然后通过将搭配点代入矩阵形式，形成了基本矩阵方程。该矩阵方程对应于线性代数方程组。通过求解该系统，确定了未知的伯努利系数，从而获得了近似解。另外，在几种温和条件下提供了基于使用伯努利多项式的误差分析。为了说明我们方法的有效性，给出了一些数值示例。

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