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Improved Error Estimates on Time-Splitting Method for the Space Fractional Klein-Gordon-Schrödinger Equation With the Small Coupling Constant
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DOI：10.1002/num.70082.png)
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Abstract
En 中文
This study aims to present the improved long-time error estimates of the space fractional Klein-Gordon-Schr & ouml;dinger equation (SFKSGE) with a small coupling parameter epsilon is an element of (0, 1]. We first turn the SFKGSE into a nonlinear coupled space fractional Schr & ouml;dinger system for numerical discretization. By the Strang splitting method, the time-splitting scheme with second-order accuracy is proposed to discretize the time domain, and it is a time-symmetric scheme. Then, the Fourier pseudo-spectral method is adopted to discretize the space domain. Through strict derivation and with the help of the regularity compensation oscillation technique, we establish the improved uniform error bound O ( & planckh;(m) + epsilon tau(2) ) for the fully discrete scheme up to the long time at O(1/epsilon), indicating an explicit expression relating the numerical errors and the coupling parameter epsilon. Combined with numerical examples, we verify that the improved uniform error bounds are sharp. The numerical results also show that the time-splitting Fourier pseudo-spectral scheme can preserve the conservation of discrete mass and have long-time stability of discrete energy. Moreover, we simulate the dynamic evolution of different soliton solutions in the SFKGSE, which further illustrates the intrinsic nonlocal interactions and heavy-tailed behavior inherent in fractional diffusion processes.
Keywords:
Fourier pseudo-spectral method
improved error estimate
regularity compensation oscillation
soliton solutions
space fractional Klein-Gordon-Schr & ouml
dinger equation
time-splitting method
weak coupling
Journal
N
IF:
1.7
Papers:
46
Citations:
3.9K