2007/04/01 by Yu. N. Kosovtsov, Kosovtsov, Yu. N. · 1 citation
Mathematics · Physics and Astronomy · #34A05 #34A34 #34A35 #FOS: Physical sciences #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical Physics (math-ph) #Numerical methods for differential equations #math-ph #math.MP #msc:34A05 #msc:34A34 #msc:34A35
paper · pdf · doi:10.48550/arxiv.0704.0072
13 pages; Submitted to the 10th International Workshop in Computer Algebra in Scientific Computing, CASC 2007
arxiv created 2007/04/01 · openalex publication_date 2007/04/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In present paper we propose seemingly new method for finding solutions of some types of nonlinear PDEs in closed form. The method is based on decomposition of nonlinear operators on sequence of operators of lower orders. It is shown that decomposition process can be done by iterative procedure(s), each step of which is reduced to solution of some auxiliary PDEs system(s) for one dependent variable. Moreover, we find on this way the explicit expression of the first-order PDE(s) for first integral of decomposable initial PDE. Remarkably that this first-order PDE is linear if initial PDE is linear in its highest derivatives. The developed method is implemented in Maple procedure, which can really solve many of different order PDEs with different number of independent variables. Examples of PDEs with calculated their general solutions demonstrate a potential of the method for automatic solving of nonlinear PDEs.