广义对称正则长波方程的守恒差分格式

A Conservative Finite Difference Scheme for Generalized Symmetric Regularized Long Wave Equations

文章考虑了具有齐次边界条件的广义对称正则长波方程的有限差分格式.提出了一个守恒并且线性非耦合的三层有限差分格式,由于格式在计算中只需要解三对角线性方程组,从而避免了其中的迭代计算.文中先讨论了一个离散守恒量,然后我们利用离散泛函分析方法证明了格式的收敛性和稳定性,从理论上得到了收敛阶为O(h^2+τ~2).通过数值试验表明,所提的方法是可靠有效的.

A finite difference method for an initial-boundary problem of Generalized Sym- metric Regularized Long-Wave （GSRLW） equations is considered here. We design a three- level linear-implicit scheme which preserves the original conservative properties for the equa- tions. The new scheme is an uncoupled, linear tri-diagonal system. Therefore, the iteration can be avoided in computing. The main idea of the method is as follows： Firstly, we discuss its discrete conservative law of an invariant. Furthermore, it is proved by the discrete en- ergy method that the scheme is unconditionally stable and second-order ceuvergent on the basis of the priori estimates. At last, we discuss the numerical analysis of the scheme about the maximal error estimate between approximation solution and numerical results and the simulations for an invariant. Numerical results demonstrate that the scheme constructed by us is efficient and reliable.