论文标题
非线性抛物线方程的高阶指数积分器，具有非平滑初始数据
A high-order exponential integrator for nonlinear parabolic equations with nonsmooth initial data
论文作者
论文摘要
提出了一个可变的步骤级多步积分器，具有对操作员值的指数函数的轮廓积分近似值，提出了用于求解使用非平滑初始数据的半连接抛物线方程的求解。通过这种方法，指数k-Step方法将在近似于温和的解决方案时具有$ k $ ther的收敛性，可能在初始时间不平整。与理论分析一致，一个数值示例表明，该方法可以在具有不连续初始数据的半线性抛物线方程的最大范围内实现高阶收敛性。
A variable stepsize exponential multistep integrator, with contour integral approximation of the operator-valued exponential functions, is proposed for solving semilinear parabolic equations with nonsmooth initial data. By this approach, the exponential k-step method would have $k$th-order convergence in approximating a mild solution, possibly nonsmooth at the initial time. In consistency with the theoretical analysis, a numerical example shows that the method can achieve high-order convergence in the maximum norm for semilinear parabolic equations with discontinuous initial data.
