A Splitting Scheme for Diffusion and Heat Conduction Problems

被引：2
|
作者：
Gladky, A. V. [1 ]
Gladka, Y. A. [2 ]
机构：
[1] Natl Acad Sci Ukraine, VM Glushkov Inst Cybernet, Kiev, Ukraine
[2] Kyiv Natl Econ Univ, Kiev, Ukraine
来源：
CYBERNETICS AND SYSTEMS ANALYSIS | 2019年 / 55卷 / 06期
关键词：
parabolic equation; optimal control problem; numerical method; splitting methods; difference scheme; stability;
D O I：
10.1007/s10559-019-00209-5
中图分类号：
TP3 [计算技术、计算机技术];
学科分类号：
0812 ;
摘要：
The problem of mathematical modeling and optimization of nonstationary diffusion and heat conduction processes is considered. An approach that uses the idea of splitting and computation of the obtained difference schemes using explicit schemes of point to point computing is proposed for numerical solution of multidimensional diffusion and heat conduction initial-boundary-value problems. Construction of difference splitting schemes, approximation and stability on initial data are investigated. Differential properties of the quality functional are analyzed for the numerical solution of the optimal control problem for a parabolic equation. An iterative algorithm for finding the optimal control is proposed.
引用
收藏
页码：988 / 998
页数：11
相关论文
共 50 条
  • [1] A Splitting Scheme for Diffusion and Heat Conduction Problems
    A. V. Gladky
    Y. A. Gladka
    [J]. Cybernetics and Systems Analysis, 2019, 55 : 988 - 998
  • [2] Group preserving scheme for backward heat conduction problems
    Liu, CS
    [J]. INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 2004, 47 (12-13) : 2567 - 2576
  • [3] A group preserving scheme for inverse heat conduction problems
    Chang, CW
    Liu, CS
    Chang, JR
    [J]. CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2005, 10 (01): : 13 - 38
  • [4] A domain splitting method for heat conduction problems in composite materials
    Hebeker, FK
    [J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2000, 34 (01): : 47 - 62
  • [5] A SPLITTING SCHEME FOR THE SOLUTION OF THE HEAT DIFFUSION EQUATION IN CYLINDRICAL COORDINATES
    SHOUCRI, MM
    NOVAK, JP
    [J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1982, 18 (08) : 1249 - 1252
  • [6] A New Optimal Scheme for Solving Nonlinear Heat Conduction Problems
    Chang, Chih-Wen
    Liu, Chein-Shan
    [J]. CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2012, 88 (04): : 269 - 291
  • [7] A time-marching MFS scheme for heat conduction problems
    Valtchev, Svilen S.
    Roberty, Nilson C.
    [J]. ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2008, 32 (06) : 480 - 493
  • [8] A NUMERICAL SCHEME BASED ON FD-RBF TO SOLVE FRACTIONAL-DIFFUSION INVERSE HEAT CONDUCTION PROBLEMS
    Wang, M. Q.
    Wang, C. X.
    Li, Ming
    Chen, C. S.
    [J]. NUMERICAL HEAT TRANSFER PART A-APPLICATIONS, 2015, 68 (09) : 978 - 992
  • [9] A linear scheme for simulating conduction heat transfer problems with nonlinear boundary conditions
    daGama, RMS
    [J]. APPLIED MATHEMATICAL MODELLING, 1997, 21 (07) : 447 - 454
  • [10] Development of numerical scheme using boundary element method for heat conduction problems
    Asghar, Ali
    Ahmad, Muhammad O.
    Bashir, Muhammad N.
    Ramzan, Muhammad
    Bashir, Muhammad Aun
    Shehzad, Sabir Ali
    [J]. PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART E-JOURNAL OF PROCESS MECHANICAL ENGINEERING, 2023,
12345