KdV方程的一类本性并行差分格式

Difference Schemes with Intrinsic Parallelism for the KdV Equation

对三阶KdV方程给出了—组非对称的差分公式,并用这些差分公式和对称的Crank-Nicolson型公式构造了一类具有本性并行的交替差分格式．证明了格式的线性绝对稳定性．对—个孤立波解、二个孤立波解和三个孤立波解的情况分别进行了数值试验,并对—个孤立波解的数值解的收敛阶和精确性进行了试验和比较．

A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. Using the schemes and the symmetric Crank-Nicolson type scheme, the alternating difference scheme for solving the KdV equation is constructed. The scheme is unconditionally stable by analysis of linearization procedure. The results of the numerical experiments for the cases of single soliton solution and double solition and triple soliton are given.