NUMERICAL ANALYSIS OF THE FRACTIONAL SEVENTH-ORDER KDV EQUATION USING AN IMPLICIT FULLY DISCRETE LOCAL DISCONTINUOUS GALERKIN METHOD

作者：Wei Leilei^*; He Yinnian; Zhang Yan

来源：International Journal of Numerical Analysis and Modeling, 2013, 10(2): 430-444.

• Time-fractional partial differential equations
• Seventh-order KdV equation
• Local discontinuous Galerkin method
• Stability
• Error estimates

In this paper an implicit fully discrete local discontinuous Galerkin (LDG) finite element method is applied to solve the time-fractional seventh-order Korteweg-de Vries (sKdV) equation, which is introduced by replacing the integer-order time derivatives with fractional derivatives. We prove that our scheme is unconditional stable and L-2 error estimate for the linear case with the convergence rate O(h(k+1) + (Delta t)(2) + (Delta t)(alpha/2) h(k+1/2)) through analysis. Extensive numerical results are provided to demonstrate the performance of the present method.

• 出版日期2013
• 单位西安交通大学