针对非线性Benjamin-Bona-Mahony (BBM)方程,在时间上构造了2阶的Backward differential formula (BDF2)时间离散格式,在空间上采用双线性单元和零阶RT单元的混合有限元方法,研究了其超收敛性质.首先,利用变换技巧给出关于逼近方程的稳...针对非线性Benjamin-Bona-Mahony (BBM)方程,在时间上构造了2阶的Backward differential formula (BDF2)时间离散格式,在空间上采用双线性单元和零阶RT单元的混合有限元方法,研究了其超收敛性质.首先,利用变换技巧给出关于逼近方程的稳定性.其次,利用逼近解的有界性得到关于其原始变量u的一个超逼近结果,进而得到其中间变量q的超逼近结果.最后利用一个算例验证理论结果的正确性.展开更多
In the present article, He＇s fractional derivative, the ansatz method, the （ C / G）-expansion method, and the exp-function method are used to construct the exact solutions of nonlinear space-time fractional Kadomts...In the present article, He＇s fractional derivative, the ansatz method, the （ C / G）-expansion method, and the exp-function method are used to construct the exact solutions of nonlinear space-time fractional Kadomtsev-Petviashvili- Benjamin-Bona Mahony （KP-BBM）. As a result, different types of exact solutions are obtained. Also we have examined the relation between the solutions obtained from the different methods. These methods are an efficient mathematical tool for solving fractional differential equations （FDEs） and it can be applied to other nonlinear FDEs.展开更多
文摘针对非线性Benjamin-Bona-Mahony (BBM)方程,在时间上构造了2阶的Backward differential formula (BDF2)时间离散格式,在空间上采用双线性单元和零阶RT单元的混合有限元方法,研究了其超收敛性质.首先,利用变换技巧给出关于逼近方程的稳定性.其次,利用逼近解的有界性得到关于其原始变量u的一个超逼近结果,进而得到其中间变量q的超逼近结果.最后利用一个算例验证理论结果的正确性.
文摘In the present article, He＇s fractional derivative, the ansatz method, the （ C / G）-expansion method, and the exp-function method are used to construct the exact solutions of nonlinear space-time fractional Kadomtsev-Petviashvili- Benjamin-Bona Mahony （KP-BBM）. As a result, different types of exact solutions are obtained. Also we have examined the relation between the solutions obtained from the different methods. These methods are an efficient mathematical tool for solving fractional differential equations （FDEs） and it can be applied to other nonlinear FDEs.
