A Fast and Stable Algorithm for Linear Parabolic Partial Differential Equations

作者：Liu, Jun^*; Jiang, Yao-Lin; Wang, Yan

来源：Numerical Algorithms, 2017, 75(3): 699-729.

DOI：10.1007/s11075-016-0217-5

• Quadratic spline collocation
• Deferred correction
• Linear parabolic PDEs
• High accuracy
• Unconditionally stable

We report a new algorithm for solving linear parabolic partial differential equations (PDEs) in one space dimension. The algorithm employs optimal quadratic spline collocation (QSC) for the space discretization and deferred correction (DC) for the time discretization. We can obtain a numerical solution with theoretical convergence order O(Delta x(4) + Delta t(min[k0+1, Nm])) by solving k(0)+1 tridiagonal linear systems at each time step, where k(0) is the number of deferred corrections per time step and Nm is usually an integer which is not bigger than 8. The stability properties of the new algorithm are analyzed, and compared with the QSC-CN0 algorithm [5], which is a very efficient algorithm. Numerical experiments are attached to demonstrate the effectiveness of the new algorithm.

• 出版日期2017-7
• 单位新疆大学; 西安交通大学; 中国石油大学（北京）