A reproducing kernel method for solving heat conduction equations with delay

被引：21

作者：

Niu, Jing ^{[1
]}

Sun, Lixia ^{[2
]}

Xu, Minqiang ^{[3
]}

Hou, Jinjiao ^{[1
]}

机构：

[1] Harbin Normal Univ, Sch Math & Sci, Harbin 150025, Heilongjiang, Peoples R China

[2] Zhejiang Univ Water Resources & Elect Power, Hangzhou 310018, Zhejiang, Peoples R China

[3] Zhejiang Univ Technol, Coll Sci, Hangzhou 310014, Zhejiang, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2020年 / 100卷

关键词：

Heat conduction equation; Delay; Reproducing kernel method; Convergence; NUMERICAL-SOLUTION; CONVERGENCE;

D O I：

10.1016/j.aml.2019.106036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We attempt to propose a numerical algorithm for the one-dimensional conduction equations with delay. Firstly, a novel reproducing kernel space satisfying the delay condition is constructed, then an approximating solution space is derived by using the orthogonal projection. In fact, the proposed scheme is a collocation method. The unique solvability as well as uniform convergence of the new scheme is discussed. Two numerical experiments are provided to illustrate our theory. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页数：7

共 50 条

[1] Solving Singularly Perturbed Multipantograph Delay Equations Based on the Reproducing Kernel Method
Geng, F. Z.
Qian, S. P.
[J]. ABSTRACT AND APPLIED ANALYSIS, 2014,
[2] A Reproducing Kernel Method for Solving Singularly Perturbed Delay Parabolic Partial Differential Equations
Xie, Ruifeng
Zhang, Jian
Niu, Jing
Li, Wen
Yao, Guangming
[J]. MATHEMATICAL MODELLING AND ANALYSIS, 2023, 28 (03) : 469 - 486
[3] SOLVING NON-LOCAL FRACTICAL HEAT EQUATIONS BASED ON THE REPRODUCING KERNEL METHOD
Li, Xiuying
Wu, Boying
[J]. THERMAL SCIENCE, 2016, 20 : S711 - S716
[4] Simplified reproducing kernel method for impulsive delay differential equations
Mei, Liangcai
Jia, Yuntao
Lin, Yingzhen
[J]. APPLIED MATHEMATICS LETTERS, 2018, 83 : 123 - 129
[5] Simplified reproducing kernel method for fractional differential equations with delay
Xu, Min-Qiang
Lin, Ying-Zhen
[J]. APPLIED MATHEMATICS LETTERS, 2016, 52 : 156 - 161
[6] Reproducing kernel method to solve fractional delay differential equations
Allahviranloo, Tofigh
Sahihi, Hussein
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2021, 400
[7] Computational method based on reproducing kernel for solving singularly perturbed differential-difference equations with a delay
Sahihi, Hussein
Abbasbandy, Saeid
Allahviranloo, Tofigh
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2019, 361 : 583 - 598
[8] Combining the complex variable reproducing kernel particle method and the finite element method for solving transient heat conduction problems
陈丽
马和平
程玉民
[J]. Chinese Physics B, 2013, 22 (05) : 71 - 78
[9] Combining the complex variable reproducing kernel particle method and the finite element method for solving transient heat conduction problems
Chen Li
Ma He-Ping
Cheng Yu-Min
[J]. CHINESE PHYSICS B, 2013, 22 (05)
[10] Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations
Mokhtari, Reza
Isfahani, Fereshteh Toutian
Mohammadi, Maryam
[J]. ABSTRACT AND APPLIED ANALYSIS, 2012,

← 1 2 3 4 5 →