论文标题
具有钢化多项内核的伏特拉整合方程的准确二阶方案的最佳误差估计值
Optimal error estimate of accurate second-order scheme for Volterra integrodifferential equations with tempered multi-term kernels
论文作者
论文摘要
在本文中，我们研究并分析了具有钢化多项内核的Volterra Integrodiffentix型方程的数值解。首先，我们得出精确解决方案的一些规律性估计。然后，通过使用曲柄 - 尼古尔森技术和产品集成（PI）规则来确定时间衍生物方案，以分别对时间衍生物和调整型的分数积分项的离散化，从中，将不均匀的网格用于克服$ t = 0 $ t = 0 $的精确解决方案的单数。根据推论的规律条件，我们证明了所提出的方案是无条件稳定的，并且在$ L_2 $ -NORM中具有准确的时间二阶收敛。数值示例证实了所提出的方法的有效性。
In this paper, we investigate and analyze numerical solutions for the Volterra integrodifferential equations with tempered multi-term kernels. Firstly we derive some regularity estimates of the exact solution. Then a temporal-discrete scheme is established by employing Crank-Nicolson technique and product integration (PI) rule for discretizations of the time derivative and tempered-type fractional integral terms, respectively, from which, nonuniform meshes are applied to overcome the singular behavior of the exact solution at $t=0$. Based on deduced regularity conditions, we prove that the proposed scheme is unconditionally stable, and possesses accurately temporal second-order convergence in $L_2$-norm. Numerical examples confirm the effectiveness of the proposed method.
