论文标题
一种新方法，以找到线性初始值问题的大致解决方案
A new approach to find an approximate solution of linear initial value problems
论文作者
论文摘要
这项工作研究了一种新方法，以找到线性初始值问题的封闭形式的分析近似解决方案。经典的Bernoulli多项式已被用来得出有限的正规多项式和有限的操作矩阵，以简化因变量的衍生物。这些正统的多项式以及相关顺序的操作矩阵提供了与线性初始值问题解决方案的良好近似值。根据问题的性质，可以获得串联形式的近似或数值近似。通过三个问题证明了该技术。将近似解决方案与可用的精确或其他数值解相提并论。在考虑到的问题的解决方案的数值中，已经注意到了高度的准确性。
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.
