论文标题
有效且快速预测的 - 矫正器方法，用于用非单明内核求解非线性分数微分方程
Efficient and fast predictor-corrector method for solving nonlinear fractional differential equations with non-singular kernel
论文作者
论文摘要
提出了有效且快速的预测 - 矫正器方法来处理非线性的caputo-fabrizio分数微分方程，其中caputo-fabrizio操作员是具有光滑内核的新型分数衍生物。所提出的方法具有二阶线性插值方案和二次插值方案的二阶方案达到均匀的精度顺序。通过使用离散的Gronwall的不平等，可以证明收敛分析。此外，应用内存项的复发关系，它减少了CPU时间执行了所提出的方法。拟议的快速算法需要大约$ o（n）$算术操作，而在常规的预测器核能方案中，$ o（n^2）$是必需的，其中$ n $是时间步长的总数。以下数值示例证明了所提出的方法的准确性以及效率。非线性分数微分方程，分数子扩散和时间折段扩散方程。理论收敛速率也通过数值实验验证。
Efficient and fast predictor-corrector methods are proposed to deal with nonlinear Caputo-Fabrizio fractional differential equations, where Caputo-Fabrizio operator is a new proposed fractional derivative with a smooth kernel. The proposed methods achieve a uniform accuracy order with the second-order scheme for linear interpolation and the third-order scheme for quadratic interpolation. The convergence analysis is proved by using the discrete Gronwall's inequality. Furthermore, applying the recurrence relation of the memory term, it reduces CPU time executed the proposed methods. The proposed fast algorithm requires approximately $O(N)$ arithmetic operations while $O(N^2)$ is required in case of the regular predictor-corrector schemes, where $N$ is the total number of time step. The following numerical examples demonstrate the accuracy of the proposed methods as well as the efficiency; nonlinear fractional differential equations, time-fraction sub-diffusion, and time-fractional advection-diffusion equation. The theoretical convergence rates are also verified by numerical experiments.
