论文标题
第二和第三阶收敛的简单数值方法，用于求解完全三阶非线性边界价值问题
A simple numerical method of second and third orders convergence for solving a fully third order nonlinear boundary value problem
论文作者
论文摘要
在本文中，我们考虑了一个完全三阶的非线性边界价值问题，这是许多研究人员的极大兴趣。首先，我们确定解决方案的存在，独特性。接下来，我们在连续和离散级别上提出简单的迭代方法。我们证明，由于使用适当的公式进行数值集成并获得总误差的估计值，因此离散方法是二阶和第三级准确性。一些示例证明了获得的理论结果和迭代方法的效率的有效性。
In this paper we consider a fully third order nonlinear boundary value problem which is of great interest of many researchers. First we establish the existence, uniqueness of solution. Next, we propose simple iterative methods on both continuous and discrete levels. We prove that the discrete methods are of second order and third accuracy due to the use of appropriate formulas for numerical integration and obtain estimate for total error. Some examples demonstrate the validity of the obtained theoretical results and the efficiency of the iterative method.
