THE ENHANCED POWER SERIES METHOD TO FIND EXACT OR APPROXIMATE SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS

This work introduces an enhanced power series method (EPSM) to find exact or approximate solutions of nonlinear differential equations. We present some case studies to show that the EPSM generates exact or highly accurate approximate solutions. The type of tested nonlinear equations are: an oscillator, a boundary value problem (BVP), a singular second-order initial value problem (IVP), an asymptotic problem, and a differential-algebraic problem. The results are comparable versus other reports from literature of semi-analytic methods, highlighting the versatility and simplicity of the EPSM.