An Alternating Group Explicit (AGE) iterative method with intrinsic parallelism is constructed based on an implicit scheme for the Regularized Long-Wave (RLW) equation. The method can be used for the iteration solutio...An Alternating Group Explicit (AGE) iterative method with intrinsic parallelism is constructed based on an implicit scheme for the Regularized Long-Wave (RLW) equation. The method can be used for the iteration solution of a general tridiagonal system of equations with diagonal dominance. It is not only easy to implement, but also can directly carry out parallel computation. Convergence results are obtained by analysing the linear system. Numerical experiments show that the theory is accurate and the scheme is valid and reliable.展开更多
A high order finite difference scheme for solving the Regularised Long Wave(RLW) equation, based on the high order Pade approximation and Lax-Wendroff type timediscretization, was developed in this paper. Some numeric...A high order finite difference scheme for solving the Regularised Long Wave(RLW) equation, based on the high order Pade approximation and Lax-Wendroff type timediscretization, was developed in this paper. Some numerical examples, including the propagation of asingle soliton, the interaction of double solitary waves and the temporal evolution of a Maxwellianinitial pulse, were studied to test the accuracy, efficiency and conservation property of thescheme. Compared with the results based on finite element methods, the scheme is proven successful.展开更多
在齐次平衡法,辅助方程法的基础上,引入新的辅助方程,借助于辅助方程的Weierstraβ椭圆函数形式的解,求出了RLW(regularized long wave)方程一类新的精确解,另外,也求得了该方程的一类特殊形式的孤立波解。这种方法也可用于寻找其它非...在齐次平衡法,辅助方程法的基础上,引入新的辅助方程,借助于辅助方程的Weierstraβ椭圆函数形式的解,求出了RLW(regularized long wave)方程一类新的精确解,另外,也求得了该方程的一类特殊形式的孤立波解。这种方法也可用于寻找其它非线性发展方程的新的精确解。展开更多
In this paper,we obtain some exact travelling wave solutions for the GF equation,the KdV Burgers equation and the RLW Burges equation with the aid of the balanced principle of the homogeneous terms.
文摘An Alternating Group Explicit (AGE) iterative method with intrinsic parallelism is constructed based on an implicit scheme for the Regularized Long-Wave (RLW) equation. The method can be used for the iteration solution of a general tridiagonal system of equations with diagonal dominance. It is not only easy to implement, but also can directly carry out parallel computation. Convergence results are obtained by analysing the linear system. Numerical experiments show that the theory is accurate and the scheme is valid and reliable.
文摘A high order finite difference scheme for solving the Regularised Long Wave(RLW) equation, based on the high order Pade approximation and Lax-Wendroff type timediscretization, was developed in this paper. Some numerical examples, including the propagation of asingle soliton, the interaction of double solitary waves and the temporal evolution of a Maxwellianinitial pulse, were studied to test the accuracy, efficiency and conservation property of thescheme. Compared with the results based on finite element methods, the scheme is proven successful.
文摘In this paper,we obtain some exact travelling wave solutions for the GF equation,the KdV Burgers equation and the RLW Burges equation with the aid of the balanced principle of the homogeneous terms.
