Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems |
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Authors: | ShunJin Wang Hua Zhang |
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Institution: | (1) Center of Theoretical Physics, Sichuan University, Chengdu, 610064, China |
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Abstract: | 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.
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, and the Center of Nuclear Physics of HIRFL of China |
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Keywords: | functional partial differential equations exact algebraic dynamics solutions of nonlinear partial differential evolution equations algebraic dynamics algorithm |
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