A reproducing kernel method for solving heat conduction equations with delay. (February 2020) - Niu, Jing; Sun, Lixia; Xu, Minqiang; Hou, Jinjiao
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.