Applying particle swarm optimization based on Padé approximant to solve ordinary differential equation

<p style='text-indent:20px;'>Ordinary differential equations are converted into a constrained optimization problems to find their approximate solutions. In this work, an algorithm is proposed by applying particle swarm (PSO) solution of ODEs based on expansion approximation. Since many cases linear and nonlinear have singularity point, Padé approximant which fractional employed for more accurate results compare Fourier Taylor expansions. The fitness function obtained adding the discrete least square weighted penalty function. applied 13 famous such as Lane Emden, Emden-Fowler, Riccati, Ivey, Abel, Thomas Fermi, Bernoulli, Bratu, Van der pol, Troesch problem other cases. offer fast methods presented in paper. demonstrate ability approach solve with initial or boundary conditions.</p>