A Newton linearized compact finite difference scheme for one class of Sobolev equations. Issue 3 (15th February 2018)

• Record Type: Journal Article
• Authors: Chen, Xiaoli; Duan, Jinqiao; Li, Dongfang
• Is Part Of: Numerical methods for partial differential equations. Volume 34:Issue 3(2018)
• Page Start: 1093
• Page End: 1112
• Publication Date: 2018-02-15
• Subjects: Newton linearized method -- finite difference method -- stability -- convergence -- Sobolev equations; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22247
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : In this article, a Newton linearized compact finite difference scheme is proposed to numerically solve a class of Sobolev equations. The unique solvability, convergence, and stability of the proposed scheme are proved. It is shown that the proposed method is of order 2 in temporal direction and order 4 in spatial direction. Moreover, compare to the classical extrapolated Crank‐Nicolson method or the second‐order multistep implicit–explicit methods, the proposed scheme is easier to be implemented as it only requires one starting value. Finally, numerical experiments on one and two‐dimensional problems are presented to illustrate our theoretical results.