论文标题
一种有效的数值方法，用于解决罗宾边界条件的两点分数非线性边界价值问题
An Efficient Numerical Approach for Solving Two-Point Fractional Order Nonlinear Boundary Value Problems with Robin Boundary Conditions
论文作者
论文摘要
本文提出了解决罗宾边界条件（RBC）的两点分数非线性边界价值问题（FN-BVP）的新策略。在新的数值方案中，将两点FNBVP转换为具有未知初始条件（ICS）的分数初始值问题（FIVP）的系统。为了近似FIVPS系统中的IC，我们根据牛顿的方法和Halley的方法开发了非线性射击方法，并使用RBC在右端进行了。为了处理系统中的FIVP，我们主要使用线性插值和二次插值来使用高阶预测器方法（HPCMS），以相当于FIVPS的Volterra积分方程。 The advantage of proposed schemes with HPCMs is that even though they are designed for solving two-point FNBVPs, they can handle both linear and nonlinear two-point Fractional order Boundary Value Problems(FBVPs) with RBCs and have uniform convergence rates of HPCMs, $O(h^2)$ and $O(h^3)$ for shooting techniques with Newton's method and Halley's method, respectively.证明了各种数值示例以确认所提出的方案的有效性和性能。另外，我们将方案的准确性和性能与另一种方法进行了比较。
This article proposes new strategies for solving two-point Fractional order Nonlinear Boundary Value Problems(FN-BVPs) with Robin Boundary Conditions(RBCs). In the new numerical schemes, a two-point FNBVP is transformed into a system of Fractional order Initial Value Problems(FIVPs) with unknown Initial Conditions(ICs). To approximate ICs in the system of FIVPs, we develop nonlinear shooting methods based on Newton's method and Halley's method using the RBC at the right end point. To deal with FIVPs in a system, we mainly employ High-order Predictor-Corrector Methods(HPCMs) with linear interpolation and quadratic interpolation into Volterra integral equations which are equivalent to FIVPs. The advantage of proposed schemes with HPCMs is that even though they are designed for solving two-point FNBVPs, they can handle both linear and nonlinear two-point Fractional order Boundary Value Problems(FBVPs) with RBCs and have uniform convergence rates of HPCMs, $O(h^2)$ and $O(h^3)$ for shooting techniques with Newton's method and Halley's method, respectively. A variety of numerical examples are demonstrated to confirm the effectiveness and performance of the proposed schemes. Also we compare the accuracy and performance of our schemes with another method.
