In this paper, taking the 2+1-dimensional sine-Gordon equation as an example, we present the concatenating method to construct the multisymplectic schemes. The method is to discretizee independently the PDEs in differ...In this paper, taking the 2+1-dimensional sine-Gordon equation as an example, we present the concatenating method to construct the multisymplectic schemes. The method is to discretizee independently the PDEs in different directions with symplectic schemes, so that the multisymplectic schemes can be constructed by concatenating those symplectic schemes. By this method, we can construct multisymplectic schemes, including some widely used schemes with an accuracy of any order. The numerical simulation on the collisions of solitons are also proposed to illustrate the efficiency of the multisymplectic schemes.展开更多
基金This work was supported by the National Natural Science Foundation of China Innovation Group(No.40221503)the CAS Hundred Talent Project,the National Key Development Planning Project for the Basic Research(No.1999032081)the National Natural Science Foundation of China(Grant No.10226012).
文摘In this paper, taking the 2+1-dimensional sine-Gordon equation as an example, we present the concatenating method to construct the multisymplectic schemes. The method is to discretizee independently the PDEs in different directions with symplectic schemes, so that the multisymplectic schemes can be constructed by concatenating those symplectic schemes. By this method, we can construct multisymplectic schemes, including some widely used schemes with an accuracy of any order. The numerical simulation on the collisions of solitons are also proposed to illustrate the efficiency of the multisymplectic schemes.
