Affiliation:
1. Sirjan University of Technology
Abstract
Abstract
This paper describes a new optimum numerical method to analyze nonlinear quadratic Riccati differential equations. To this end, the Finite Difference Method (FDM) is employed to extract an appropriate discretized objective function, and the penalty method is implemented to convert the constrained problem into an unconstrained one via satisfying the initial conditions. Furthermore, the High Exploration Particle Swarm Optimization (HEPSO) is utilized to find the best numerical values of the nonlinear quadratic Riccati differential equation. In order to illustrate the effectiveness of HEPSO, the optimization trajectories are compared with those of a standard Particle Swarm Optimization (PSO) algorithm. Moreover, comparisons are made between Adomians decomposition method (ADM), Homotopy Perturbation Method (HPM), the exact solution and the proposed method to expose the accuracy, effectiveness and simplicity of the proposed method.
Publisher
Research Square Platform LLC
Reference29 articles.
1. A family of embedded Runge-Kutta formulae;Dormand JR;J Comput Appl Math,1980
2. Implementation of Gauss-Jackson integration for orbit propagation;Berry MM;J Astronaut Sci,2004
3. Solving Riccati differential equation using Adomian’s decomposition method;El-Tawil MA;Appl Math Comput,2004
4. Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian’s decomposition method;Abbasbandy S;Appl Math Comput,2006
5. A numerical approach for fractional order Riccati differential equation using B-Spline operational matrix;Hossein J;Fract Calculus Appl Anal,2015