论文标题
用于求解非线性二氢方程的第四阶收敛的数值方法和数值方法
Existence results and numerical method of fourth order convergence for solving a nonlinear triharmonic equation
论文作者
论文摘要
在这项工作中，我们考虑了非线性二氢方程的边界价值问题。由于非线性术语的非线性边界价值问题减少了运算符方程，因此我们确定了解决方案的存在，独特性和阳性。更重要的是，我们在连续和离散级别上设计了问题的迭代方法，以解决问题的数值解决方案。对获得的离散解决方案的实际总误差进行分析。一些示例证明了理论结果在定性方面和迭代方法的效率上的适用性。
In this work, we consider a boundary value problem for nonlinear triharmonic equation. Due to the reduction of nonlinear boundary value problems to operator equation for nonlinear terms we establish the existence, uniqueness and positivity of solution. More importantly, we design an iterative method at both continuous and discrete level for numerical solution of the problem. An analysis of actual total error of the obtained discrete solution is made. Some examples demonstrate the applicability of the theoretical results on qualitative aspects and the efficiency of the iterative method.
