求线性初值问题近似解的一种新方法
A new approach to find an approximate solution of linear initial value problems
摘要：
本文研究了一种求线性初值问题封闭形式解析近似解的新方法。经典的伯努利多项式被用来导出一个有限的标准正交多项式集和一个有限的运算矩阵来简化因变量的导数。这些正交多项式与相关阶的运算矩阵一起提供了线性初值问题的解的良好近似。根据问题的性质，可以得到级数形式的近似或数值逼近。该技术已通过三个问题得到证明。将近似解与现有的精确解或其他数值解进行了比较。高精度已注意到在数值的解决方案所考虑的问题。
英文摘要：
This work investigates a new approach to find closed form analytical approximate solution of linear initial value problems. Classical Bernoulli polynomials have been used to derive a finite set of orthonormal polynomials and a finite operational matrix to simplify derivatives of dependent variable. These orthonormal polynomials together with the operational matrix of relevant order provides a good approximation to the solution of a linear initial value problem. Depending upon the nature of a problem, a series form approximation or numerical approximation can be obtained. The technique has been demonstrated through three problems. Approximate solutions have been compared with available exact or other numerical solutions. High degree of accuracy has been noted in numerical values of solutions for considered problems.
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