求解线性边值问题的一种新的运算矩阵技术
A new operational matrix technique to solve linear boundary value problems
摘要：
提出了一种求解一类线性边值问题的新方法。技术主要基于从一组修改的伯努利多项式开发的运算矩阵。新的一组多项式是一个正交规范集与Gram-Schmidt正交化应用于经典的伯努利多项式。该方法将给定的线性边值问题转化为一个代数方程组，通过求解该方程组，得到边值问题的一个多项式形式的近似解。该技术被应用到四个问题，得到的近似解以图形方式进行比较，可用的精确和其他数值解。该方法比许多现有的方法简单，并提供了高度的准确性。
英文摘要：
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.
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。
