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A diagonal splitting method for solving semidiscretized parabolic partial differential equations
Author(s) -
Hosseini Rasool,
Tatari Mehdi
Publication year - 2020
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22427
Subject(s) - mathematics , parabolic partial differential equation , partial differential equation , diagonal , mathematical analysis , heat equation , generalization , ftcs scheme , stability (learning theory) , work (physics) , norm (philosophy) , ordinary differential equation , differential equation , differential algebraic equation , geometry , mechanical engineering , machine learning , computer science , law , political science , engineering
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.