论文标题
准中性操作员和分数差异问题的解决方案
Quasi-Interpolant Operators and the Solution of Fractional Differential Problems
论文作者
论文摘要
如今，分数微分方程是建立现实世界现象的良好工具。由于分析解决方案很少可用，因此在为其解决方案构建有效的数值方法方面付出了巨大的努力。在本文中，我们有兴趣解决具有分数顺序的空间导数的边界价值问题。为此，我们提出了一种搭配方法，其中分数问题的解决方案由样条型准互助操作员近似。这使我们能够以一种简单的方式构建数值解决方案。我们通过一些数值测试表明，所提出的方法是有效且准确的。
Nowadays, fractional differential equations are a well established tool to model phenomena from the real world. Since the analytical solution is rarely available, there is a great effort in constructing efficient numerical methods for their solution. In this paper we are interested in solving boundary value problems having space derivative of fractional order. To this end, we present a collocation method in which the solution of the fractional problem is approximated by a spline quasi-interpolant operator. This allows us to construct the numerical solution in an easy way. We show through some numerical tests that the proposed method is efficient and accurate.
