Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems  

作　　者：WANG ShunJin ZHANG Hua 

机构地区：[1]Center of Theoretical Physics,Sichuan University,Chengdu 610064,China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2008年第6期577-590,共14页中国科学：物理学、力学、天文学（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant Nos. 10375039, 10775100 and 90503008);the Doctoral Program Foundation of the Ministry of Education of China,;the Center of Nuclear Physics of HIRFL of China

摘　　要：Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.Using functional derivative technique in quantum field theory, the algebraic dynamics approach for solution of ordinary differential evolution equations was generalized to treat partial differential evolution equations. The partial differential evolution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynamics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new numerical algorithm—algebraic dynamics algorithm was proposed for partial differential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experiments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.

关 键 词：functional PARTIAL DIFFERENTIAL EQUATIONS exact ALGEBRAIC DYNAMICS SOLUTIONS of nonlinear PARTIAL DIFFERENTIAL evolution EQUATIONS ALGEBRAIC DYNAMICS algorithm 

分 类 号：O193[理学—数学] O175[理学—基础数学]