Department of Mathematics, Wollega University, Nekemte, Ethiopia.
Department of Mathematics, Jimma University, Jimma, Ethiopia.
BMC Res Notes. 2022 Jun 3;15(1):195. doi: 10.1186/s13104-022-06078-0.
The main aim of this paper is to develop a linear B-spline finite element method for solving generalized diffusion equations with delay. The linear B-spline basis function is used to discretize the space variable. The time discretization process is based on Crank-Nicolson. The benefit of the scheme is that the numerical solution is obtained as a smooth piecewise continuous function which empowers one to find an approximate solution at any desired position in the domain.
Sufficient and necessary conditions for the numerical method to be asymptotically stable are derived. The convergence of the numerical method is studied. Some numerical experiments are performed to verify the applicability of the numerical method.
本文的主要目的是开发一种求解时滞广义扩散方程的线性 B 样条有限元方法。线性 B 样条基函数用于离散空间变量。时间离散过程基于 Crank-Nicolson 方法。该方案的优点是数值解是一个平滑的分段连续函数，这使得我们能够在域中的任何期望位置找到近似解。
推导出了数值方法渐近稳定的充分必要条件。研究了数值方法的收敛性。进行了一些数值实验来验证数值方法的适用性。
