论文标题
完全第四阶非线性功能微分方程的存在结果和数值解
Existence results and numerical solution of fully fourth order nonlinear functional differential equations
论文作者
论文摘要
在本文中，我们考虑了完全第四阶非线性功能微分方程的边界价值问题，该方程包含所有比例延迟参数的较低衍生物。通过将问题减少到右侧非线性函数的运算符方程，我们在连续和离散级别上建立了解决方案的存在和独特性，并构建了迭代方法以解决它。我们获得离散迭代解决方案的总误差估计。许多例子证明了获得的理论结果的有效性和数值方法的效率。
In this paper we consider a boundary value problem for fully fourth order nonlinear functional differential equation which contains all lower derivatives of proportional delay arguments. By the reduction of the problem to operator equation for the right hand side nonlinear function we establish the existence and uniqueness of solution and construct iterative methods on both continuous and discrete levels for solving it. We obtain the total error estimate for the discrete iterative solution. Many examples demonstrate the validity of the obtained theoretical results and the efficiency of the numerical method.
