The Splitting Crank–Nicolson Scheme with Intrinsic Parallelism for Solving Parabolic Equations. (30th March 2020)

• Record Type: Journal Article
• Authors: Xue, Guanyu; Gong, Yunjie; Feng, Hui
• Other Names: Wang Liguang Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-03-30
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/8571625
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this paper, a splitting Crank–Nicolson (SC-N) scheme with intrinsic parallelism is proposed for parabolic equations. The new algorithm splits the Crank–Nicolson scheme into two domain decomposition methods, each one is applied to compute the values at ( n + 1)th time level by use of known numerical solutions at n -th time level, respectively. Then, the average of the above two values is chosen to be the numerical solutions at ( n + 1)th time level. The new algorithm obtains accuracy of the Crank–Nicolson scheme while maintaining parallelism and unconditional stability. This algorithm can be extended to solve two-dimensional parabolic equations by alternating direction implicit (ADI) technique. Numerical experiments illustrate the accuracy and efficiency of the new algorithm.