A diagonal splitting method for solving semidiscretized parabolic partial differential equations. Issue 2 (30th August 2019)

• Record Type: Journal Article
• Authors: Hosseini, Rasool; Tatari, Mehdi
• Is Part Of: Numerical methods for partial differential equations. Volume 36:Issue 2(2020)
• Page Start: 268
• Page End: 283
• Publication Date: 2019-08-30
• Subjects: advection–diffusion equation -- heat equation -- maximum principle -- splitting methods -- system of ordinary differential equations; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22427
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: In this work, a diagonal splitting idea is presented for solving linear systems of ordinary differential equations. The resulting methods are specially efficient for solving systems which have arisen from semidiscretization of parabolic partial differential equations (PDEs). Unconditional stability of methods for heat equation and advection–diffusion equation is shown in maximum norm. Generalization of the methods in higher dimensions is discussed. Some illustrative examples are presented to show efficiency of the new methods.