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

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 fu...

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Bibliographic Details
Published in:Science China. Physics, mechanics & astronomy Vol. 51; no. 6; pp. 577 - 590
Main Authors: Wang, ShunJin, Zhang, Hua
Format: Journal Article
Language:English
Published: Heidelberg SP Science in China Press 01.06.2008
Springer Nature B.V
Subjects:
Algebra
Algorithms
Astronomy
Burgers equation
Classical and Continuum Physics
Differential equations
Dynamical systems
Evolutionary computation
Exact solutions
Nonlinear dynamics
Numerical analysis
Observations and Techniques
Operators (mathematics)
Partial differential equations
Physics
Physics and Astronomy
Quantum field theory
Quantum theory
Taylor series
exact algebraic dynamics solutions of nonlinear partial differential evolution equations
algebraic dynamics algorithm
functional partial differential equations
ISSN:1672-1799, 1674-7348, 1862-2844, 1869-1927
Online Access:Get full text
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Summary: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.
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ISSN:1672-1799
1674-7348
1862-2844
1869-1927
DOI:10.1007/s11433-008-0055-0