A Novel Representation of the Exact Solution for Differential Algebraic Equations System Using Residual Power-Series Method

Abstract

We implement a relatively new analytic iterative technique to get approximate solutions of differential algebraic equations system based on generalized Taylor series formula. The solution methodology is based on generating the residual power series expansion solution in the form of a rapidly convergent series with easily computable components. The residual power series method (RPSM) can be used as an alternative scheme to obtain analytical approximate solution of different types of differential algebraic equations system applied in mathematics. Simulations and test problems were analyzed to demonstrate the procedure and confirm the performance of the proposed method, as well as to show its potentiality, generality, viability, and simplicity. The results reveal that the proposed method is very effective, straightforward, and convenient for solving different forms of such systems.

Computational Optimization of Residual Power Series Algorithm for Certain Classes of Fuzzy Fractional Differential Equations

“…Furthermore, the RPS is characterized as an applicable and easy technique to create power series solutions for strongly linear and nonlinear equations without being linearized, discretized, or exposed to perturbation [23][24][25][26][27]. Unlike the classical power series method, the RPS neither requires comparing the corresponding coefficients nor is a recursion relation needed as well.…”

Hybrid Block Method for Direct Numerical Approximation of Second Order Initial Value Problems Using Taylor Series Expansions

“…Differential equations of this form play an important role in modeling virtually every physical or biological process because such equations occur in connection with numerous problems that are encountered in various aspects of our everyday life. This concept of mathematical modeling involves translating problems from an application area into tractable mathematical formulations whose theoretical and numerical analysis provide insight, answers and guidance useful for the originating application (Abdelrahim and Omar, 2016;Moaddy et al, 2015).…”

Approximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform Method

“…For examples of these methods, we refer to the work in (Hesameddini and Fotros, 2012;Moaddy et al, 2011;Abdulaziz et al, 2008;Hashim et al, 2009;Odibat and Momani, 2006;Khalil et al, 2015a;2015b;2015c;El-Ajou et al, 2015;Abu-Gdairi et al, 2015;Freihat and Al-Smadi, 2013;Momani et al, 2014;Al-Smadi et al, 2013;. On the other hand, many applications for different problems by using other numerical algorithms can be found in (Abu Arqub et al, 2012;Abu Arqub and Al-Smadi, 2014;Moaddy et al, 2015;Komashynska and Al-Smadi, 2014;Komashynska et al, 2016).…”