Abd-Elhameed Waleed M, Doha Eid H, Bassuony Mahmoud A
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia ; Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt.
Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt.
ScientificWorldJournal. 2014 Jan 23;2014:309264. doi: 10.1155/2014/309264. eCollection 2014.
Two numerical algorithms based on dual-Petrov-Galerkin method are developed for solving the integrated forms of high odd-order boundary value problems (BVPs) governed by homogeneous and nonhomogeneous boundary conditions. Two different choices of trial functions and test functions which satisfy the underlying boundary conditions of the differential equations and the dual boundary conditions are used for this purpose. These choices lead to linear systems with specially structured matrices that can be efficiently inverted, hence greatly reducing the cost. The various matrix systems resulting from these discretizations are carefully investigated, especially their complexities and their condition numbers. Numerical results are given to illustrate the efficiency of the proposed algorithms, and some comparisons with some other methods are made.
开发了两种基于对偶彼得罗夫-伽辽金方法的数值算法，用于求解由齐次和非齐次边界条件控制的高阶边值问题（BVP）的积分形式。为此，使用了两种不同的试函数和检验函数选择，它们满足微分方程的基本边界条件和对偶边界条件。这些选择导致具有特殊结构矩阵的线性系统，这些矩阵可以有效地求逆，从而大大降低了成本。仔细研究了这些离散化产生的各种矩阵系统，特别是它们的复杂性和条件数。给出了数值结果以说明所提算法的效率，并与其他一些方法进行了比较。
