论文标题
耦合分数非线性klein-gordon-schrödinger方程的保守光谱盖金方法的无条件收敛
Unconditional convergence of conservative spectral Galerkin methods for the coupled fractional nonlinear Klein-Gordon-Schrödinger equations
论文作者
论文摘要
在这项工作中，提出了两种新型的结构传播光谱Galerkin方法，这些方法基于曲柄 - 尼科尔森方案和指数标量辅助变量方法，用于求解耦合的分数非线性klein klein-glein-gordon-gordon-schrödinger方程。本文着重于所提出的方案的理论分析和计算效率，事实证明，曲柄 - 尼古隆方案是无条件的收敛性，并且具有数值溶液的最大符号界限。指数标量辅助变量方案是线性隐式和解耦的，但缺乏最大符号界限，也已经修改了能量结构。随后，详细介绍了提出的方案的有效实施。理论分析和数值比较都表明，在长期计算中，提出的光谱Galerkin方法具有很高的效率。
In this work, two novel classes of structure-preserving spectral Galerkin methods are proposed which based on the Crank-Nicolson scheme and the exponential scalar auxiliary variable method respectively, for solving the coupled fractional nonlinear Klein-Gordon-Schrödinger equation. The paper focuses on the theoretical analyses and computational efficiency of the proposed schemes, the Crank-Nicoloson scheme is proved to be unconditionally convergent and has the maximum-norm boundness of numerical solutions. The exponential scalar auxiliary variable scheme is linearly implicit and decoupled, but lack of the maximum-norm boundness, also, the energy structure has been modified. Subsequently, the efficient implementations of the proposed schemes are introduced in detail. Both the theoretical analyses and the numerical comparisons show that the proposed spectral Galerkin methods have high efficiency in long-time computations.
