A reproducing kernel method for solving heat conduction equations with delay. (February 2020)

• Record Type: Journal Article
• Authors: Niu, Jing; Sun, Lixia; Xu, Minqiang; Hou, Jinjiao
• Is Part Of: Applied mathematics letters. Volume 100(2020)
• Publication Date: 2020-02
• Subjects: Heat conduction equation -- Delay -- Reproducing kernel method -- Convergence; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2019.106036
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: 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.