[1]½¯³¯Áú,Ëィǿ,ºÎÑ··å,µÈ.KdV·½³ÌµÄ¸ß½×±£ÄÜÁ¿Ëã·¨[J].ÄϾ©Ê¦·¶´óѧѧ±¨(×ÔÈ»¿Æѧ°æ),2017,40(04):16.[doi:10.3969/j.issn.1001-4616.2017.04.004]
¡¡Jiang Chaolong,Sun Jianqiang,He Xunfeng,et al.High Order Energy-Preserving Method for the KdV Equation[J].Journal of Nanjing Normal University(Natural Science Edition),2017,40(04):16.[doi:10.3969/j.issn.1001-4616.2017.04.004]
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2017-12-30

ÎÄÕÂÐÅÏ¢/Info

Title:
High Order Energy-Preserving Method for the KdV Equation
ÎÄÕ±àºÅ:
1001-4616(2017)04-0016-05
×÷Õß:
½¯³¯ÁúËィǿºÎÑ··åãƾ²Ò¶
º£ÄÏ´óѧÐÅÏ¢¿Æѧ¼¼ÊõѧԺ,º£ÄÏ º£¿Ú 570228
Author(s):
Jiang ChaolongSun JianqiangHe XunfengYan Jingye
College of Information Science and Technology,Hainan University,Haikou 570228,China
¹Ø¼ü´Ê:
AVF·½·¨KdV·½³Ì±£ÄÜÁ¿Ëã·¨
Keywords:
AVF methodKdV equationenergy-preserving method
·ÖÀàºÅ:
O241
DOI:
10.3969/j.issn.1001-4616.2017.04.004
ÎÄÏ×±êÖ¾Âë:
A
ÕªÒª:
KdV·½³Ì±»×ª»¯ÎªÎÞÇîάHamiltonϵͳ,Ôڿռ䷽ÏòÉÏÓÃÄâÆ×Ëã·¨ÀëÉ¢µÃµ½ÁËKdV·½³ÌµÄÓÐÏÞάHamiltonϵͳ. ÀûÓÃËĽ×ƽ¾ùÏòÁ¿³¡(AVF)·½·¨ÀëÉ¢KdV·½³ÌµÄÓÐÏÞάHamiltonϵͳ,¹¹ÔìÁËKdV·½³ÌµÄ¸ß½×±£ÄÜÁ¿¸ñʽ. ÀûÓù¹ÔìµÄ¸ß½×±£ÄÜÁ¿¸ñʽÊýֵģÄâ¹ÂÁ¢²¨µÄÑÝ»¯ÐÐΪ. ÊýÖµ½á¹û±íÃ÷,¸ß½×±£ÄÜÁ¿¸ñʽ¿ÉÒÔ¾«È·±£³Ö·½³ÌµÄÀëÉ¢ÄÜÁ¿Êغã.
Abstract:
The KdV equation is transformed into an infinite dimensional Hamiltonian system. The finite dimensional Hamiltonian system of the KdV equation is obtained by the pseudo-spectral method in spacial direction. Then,the finite dimensional Hamiltonian system is discretizated by the fourth order AVF method. Thus,a high order energy-preserving scheme of the KdV equation is derived. The evolution of the solitary wave is simulated by the high order energy-preserving scheme. Numerical results show that the proposed scheme can preserve the discrete energy of the KdV equation exactly.

²Î¿¼ÎÄÏ×/References:

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