论文标题
日志正交函数：近似属性和应用程序
Log orthogonal functions: approximation properties and applications
论文作者
论文摘要
我们提出了两个新类正交函数类别，即原木正交函数（LOFS）和广义的日志正交函数（GLOF），这些功能是通过将$ \ log $映射应用于laguerre polynomials构建的。我们为这些新的正交函数开发了基本近似理论，并将它们应用于求解溶液表现出较弱奇异性的几个典型分数微分方程。我们的错误分析和数值结果表明，基于新的正交函数的方法特别适用于一个端点的奇异性较弱的函数，并且如果使用通常的正交多项式，则可以导致指数的收敛速率，而不是代数率低。
We present two new classes of orthogonal functions, log orthogonal functions (LOFs) and generalized log orthogonal functions (GLOFs), which are constructed by applying a $\log$ mapping to Laguerre polynomials. We develop basic approximation theory for these new orthogonal functions and apply them to solve several typical fractional differential equations whose solutions exhibit weak singularities. Our error analysis and numerical results show that our methods based on the new orthogonal functions are particularly suitable for functions which have weak singularities at one endpoint, and can lead to exponential convergence rate, as opposed to low algebraic rates if usual orthogonal polynomials are used.
