A Numerical Method of High Accuracy for Linear Parabolic Partial Differential Equations

作者：Liu, Jun^*; Wang, Yan

来源：Mathematical Problems in Engineering, 2012, 2012: 497365.

DOI：10.1155/2012/497365

• QUADRATIC-SPLINE COLLOCATION
• SCALING FUNCTIONS

We report a new numerical algorithm for solving one-dimensional linear parabolic partial differential equations (PDEs). The algorithm employs optimal quadratic spline collocation (QSC) for the space discretization and two-stage Gauss method for the time discretization. The new algorithm results in errors of fourth order at the gridpoints of both the space partition and the time partition, and large time steps are allowed to save computational cost. The stability of the new algorithm is analyzed for a model problem. Numerical experiments are carried out to confirm the theoretical order of accuracy and demonstrate the effectiveness of the new algorithm.

• 出版日期2012
• 单位西安交通大学; 中国石油大学（北京）