A compact locally one‐dimensional finite difference method for nonhomogeneous parabolic differential equations

This paper is concerned with accurate and efficient numerical methods for solving parabolic differential equations. A compact locally one‐dimensional finite difference method is presented, which has second‐order accuracy in time and fourth‐order accuracy in space with respect to discrete H 1 norm and L 2 norm. The scheme is proved to be unconditionally stable. All computations are implemented in one direction and the CPU time is relatively smaller compared with some other compact computational schemes. Numerical results are presented to show the accuracy and efficiency of the new algorithm for the parabolic differential equations. Copyright © 2009 John Wiley & Sons, Ltd.