数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (4): 971-988.doi: 10.1007/s10473-019-0405-1

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ECONOMICAL DIFFERENCE SCHEME FOR ONE MULTI-DIMENSIONAL NONLINEAR SYSTEM

Temur JANGVELADZE1,2, Zurab KIGURADZE1,3, Mikheil GAGOSHIDZE1,2   

  1. 1. Ilia Vekua Institute of Applied Mathematics, Ivane Javakhishvili Tbilisi State University, 2 University St. 0186, Tbilisi, Georgia;
    2. Georgian Technical University, 77 Kostava Ave. 0175, Tbilisi, Georgia;
    3. Missouri University Science and Technology, Department of Electrical and Computer Engineering, Electromagnetic Compatibility Laboratory, 4000 Enterprise Drive, 65409 Rolla, MO, USA
  • 收稿日期:2017-12-12 出版日期:2019-08-25 发布日期:2019-09-12
  • 作者简介:Temur JANGVELADZE,E-mail:temur.jangveladze@tsu.ge,t.jangveladze@gtu.ge,tjangv@yahoo.com;Zurab KIGURADZE,E-mail:kiguradzz@mst.edu,zkigur@yahoo.com;Mikheil GAGOSHIDZE,E-mail:mikheil.gagoshidze@tsu.ge,m.gagoshidze@gtu.ge,mishagagoshidze@gmail.com

ECONOMICAL DIFFERENCE SCHEME FOR ONE MULTI-DIMENSIONAL NONLINEAR SYSTEM

Temur JANGVELADZE1,2, Zurab KIGURADZE1,3, Mikheil GAGOSHIDZE1,2   

  1. 1. Ilia Vekua Institute of Applied Mathematics, Ivane Javakhishvili Tbilisi State University, 2 University St. 0186, Tbilisi, Georgia;
    2. Georgian Technical University, 77 Kostava Ave. 0175, Tbilisi, Georgia;
    3. Missouri University Science and Technology, Department of Electrical and Computer Engineering, Electromagnetic Compatibility Laboratory, 4000 Enterprise Drive, 65409 Rolla, MO, USA
  • Received:2017-12-12 Online:2019-08-25 Published:2019-09-12

摘要: The multi-dimensional system of nonlinear partial differential equations is considered. In two-dimensional case, this system describes process of vein formation in higher plants. Variable directions finite difference scheme is constructed. The stability and convergence of that scheme are studied. Numerical experiments are carried out. The appropriate graphical illustrations and tables are given.

关键词: System of nonlinear partial differential equations, variable directions finite difference scheme, stability and convergence, numerical resolution

Abstract: The multi-dimensional system of nonlinear partial differential equations is considered. In two-dimensional case, this system describes process of vein formation in higher plants. Variable directions finite difference scheme is constructed. The stability and convergence of that scheme are studied. Numerical experiments are carried out. The appropriate graphical illustrations and tables are given.

Key words: System of nonlinear partial differential equations, variable directions finite difference scheme, stability and convergence, numerical resolution

中图分类号: 

  • 65M06