论文标题
非线性分数微分方程的高阶方案的数值分析，精度均匀
Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy
论文作者
论文摘要
我们引入了使用Caputo衍生物的分数普通微分方程的高阶数值方案。该方法是通过将域将域分为多个子间隔的，并在每个子间隙上应用二次插值来开发。该方法被证明是无条件稳定的，对于一般的非线性方程，均匀的尖锐数值$ 3-ν$可以严格证明，以便在所有时间步骤中进行足够平滑的解决方案。该证明为在非线性情况下证明高阶方案的急剧顺序提供了一般指南。给出了一些数值示例以验证我们的理论结果。
We introduce a high-order numerical scheme for fractional ordinary differential equations with the Caputo derivative. The method is developed by dividing the domain into a number of subintervals, and applying the quadratic interpolation on each subinterval. The method is shown to be unconditionally stable, and for general nonlinear equations, the uniform sharp numerical order $3-ν$ can be rigorously proven for sufficiently smooth solutions at all time steps. The proof provides a general guide for proving the sharp order for higher-order schemes in the nonlinear case. Some numerical examples are given to validate our theoretical results.
