非线性时间分数Klein-Gordon型方程的一种线性化二阶方案
A linearized second-order scheme for nonlinear time fractional Klein-Gordon type equations
AI总结：
本文提出一种线性化二阶方案解决非线性时间分数Klein-Gordon型方程，避免迭代方法，通过引入新网格函数和近期研究思想，证明方法在时间上具有二阶精度。
摘要：
本文考虑非线性时间分数Klein-Gordon型方程的差分方案。提出一种线性化方案来解决该问题。结果表明，无需采用迭代方法。分析中的主要困难在于离散化过程中考虑了某些近似解的加权平均，标准能量估计无法直接应用。通过引入一个新的网格函数，进一步近似解，并利用一些近期研究中的思想，我们证明该方法在时间上具有二阶精度。
英文摘要：
We consider difference schemes for nonlinear time fractional Klein-Gordon type equations in this paper. A linearized scheme is proposed to solve the problem. As a result, iterative method need not be employed. One of the main difficulties for the analysis is that certain weight averages of the approximated solutions are considered in the discretization and standard energy estimates cannot be applied directly. By introducing a new grid function, which further approximates the solution, and using ideas in some recent studies, we show that the method converges with second-order accuracy in time.
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