论文标题
使用时间折阻的Westervelt方程的时间步变方法的数值分析
Numerical analysis of a time-stepping method for the Westervelt equation with time-fractional damping
论文作者
论文摘要
我们以非线性声学中的一个重要方程式开发了一种数值方法，其形式是衰减在时间运算符中由一类非本地的衰减表示的形式。陈述和分析了基于梯形规则和A稳定卷积正交的时间的半差异。连续方程的存在和规律性分析介绍了半混凝土系统的稳定性和误差分析。错误分析包括考虑$ t = 0 $的奇异性，这是通过在数值方案中使用校正来解决的。广泛的数值实验证实了这一理论。
We develop a numerical method for the Westervelt equation, an important equation in nonlinear acoustics, in the form where the attenuation is represented by a class of non-local in time operators. A semi-discretisation in time based on the trapezoidal rule and A-stable convolution quadrature is stated and analysed. Existence and regularity analysis of the continuous equations informs the stability and error analysis of the semi-discrete system. The error analysis includes the consideration of the singularity at $t = 0$ which is addressed by the use of a correction in the numerical scheme. Extensive numerical experiments confirm the theory.
