论文标题
一种解决线性边界价值问题的新操作矩阵技术
A new operational matrix technique to solve linear boundary value problems
论文作者
论文摘要
提出了一种新技术来解决一类线性边界值问题（BVP）。技术主要基于从一组修改的Bernoulli多项式开发的操作矩阵。新的多项式集是使用革兰氏阴性正交化获得的正顺序集，该集合应用于经典的Bernoulli多项式。所介绍的方法将给定的线性BVP更改为代数方程系统，该系统被求解以找到BVP的近似解，以所需程度的多项式形式。将该技术应用于四个问题，并以图形方式将获得的近似解决方案与可用的精确和其他数值解决方案进行比较。该方法比许多现有方法更简单，并且提供了高度的准确性。
A new technique is presented to solve a class of linear boundary value problems (BVP). Technique is primarily based on an operational matrix developed from a set of modified Bernoulli polynomials. The new set of polynomials is an orthonormal set obtained with Gram-Schmidt orthogonalization applied to classical Bernoulli polynomials. The presented method changes a given linear BVP into a system of algebraic equations which is solved to find an approximate solution of BVP in form of a polynomial of required degree. The technique is applied to four problems and obtained approximate solutions are graphically compared to available exact and other numerical solutions. The method is simpler than many existing methods and provides a high degree of accuracy.
