An improved approximate analytic solution for Riccati equations over extended intervals. (English) Zbl 1310.34022

Summary: In this paper, we present a new effective approach based on our previous method for solving Riccati equations [A. R. Vahidi and M Didgar, “An improved method for determining the solution of Riccati equations”, Neural Comput. Appl. 23, No. 5, 1229–1237 (2013; doi:10.1007/s00521-012-1064-5)]. The proposed technique combines transformation of variables with the Laplace Adomian decomposition method, which is a variant of the classic Adomian decomposition method. The method examined practicality for several specific examples of the Riccati equation. Numerical results show that the proposed method is more efficient and accurate than other applied methods over extended intervals, and stands in good agreement to the exact solutions. The obtained results provide a rapidly convergent series, from which we achieve a high degree of accuracy using only a few terms of the recursion scheme. Thus we have developed a natural sequence of rational approximations as a technique of solution continuation for the Riccati equation.


34A45 Theoretical approximation of solutions to ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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