基于伯努利多项式的新型运算矩阵
A new operational matrix based on Bernoulli polynomials
AI总结：
本文提出基于伯努利多项式的运算矩阵，用于将微分方程转化为代数方程组，通过数值实例验证了该方法的计算效率和精度。
摘要：
在本研究中，引入了伯努利多项式，并利用其性质构建积分、导数和乘法的运算矩阵。这些性质被用来将微分方程转换为矩阵方程，对应于具有未知伯努利系数的代数方程组。该方法可用于解决微分方程、积分方程等问题。数值示例表明，该方法计算简便，且展示了方法的效率和准确性。
英文摘要：
In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized to transform the differential equation to a matrix equation which corresponds to a system of algebraic equations with unknown Bernoulli coefficients. This method can be used for many problems such as differential equations, integral equations and so on. Numerical examples show the method is computationally simple and also illustrate the efficiency and accuracy of the method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
