Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 497365, 14 pages
Research Article

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

Jun Liu1,2 and Yan Wang1

1College of Science, China University of Petroleum, Qingdao, Shandong 266580, China
2Department of Mathematical Sciences, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China

Received 23 December 2011; Accepted 17 June 2012

Academic Editor: Kwok-Wo Wong

Copyright © 2012 Jun Liu and Yan Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.