论文标题
在半线上用于初始有限价值问题的数值统一变换方法
The Numerical Unified Transform Method for Initial-boundary Value Problems on the Half-line
论文作者
论文摘要
我们将fokas的统一变换方法作为一种数值方法来求解半行上的线性偏微分方程。该方法在任何X和T上计算解决方案，而无需空间离散或时间步进时间。借助轮廓变形和振荡整合技术，该方法的复杂性在大X，T中不会增加，并且该方法随着X，t的增加而更准确。我们的目标是在（x，t）平面的大区域中保持高精度，在保持高精度的同时，不对初始或边界函数的功能形式进行任何假设。
We implement the Unified Transform Method of Fokas as a numerical method to solve linear partial differential equations on the half-line. The method computes the solution at any x and t without spatial discretization or time stepping. With the help of contour deformations and oscillatory integration techniques, the method's complexity does not increase for large x,t and the method is more accurate as x,t increase. Our goal is to make no assumptions on the functional form of the initial or boundary functions while maintaining high accuracy in a large region of the (x,t) plane.
