Adaptive LMS power series analytical solution for differential algebraic equations

Differential Algebraic Equations (DAEs) are essential in the analysis of many engineering, physical, chemical and mathematical systems. Numerical methods are popular to solve highly nonlinear and even linear DAEs. On the other hand, analytical solutions for DAEs are very limited. This work presents an efficient analytical solution for DAEs based on power series regressions. The coefficients of the estimated power series solution are adaptively computed employing the computationally simple signed least mean squares adaptive algorithm. The DAEs are assumed to be on the general implicit canonical form. The proposed adaptive power series method can solve linear and nonlinear DAEs systems. The efficient and accurate solutions provided by the technique proposed are illustrated through simulated examples. It is shown that the performance of the technique proposed outperforms existing conventional and modern methods.