Int. J. Appl. Comput. Math (2020) 6:26 https://doi.org/10.1007/s40819-020-0774-0 ORIGINAL PAPER New Algorithm for Solving Non-linear Functional Equations Manoj Kumar 1,2 · Aman Jhinga 1 · Varsha Daftardar-Gejji 1 © Springer Nature India Private Limited 2020 Abstract The new iterative method (DGJ) proposed by Daftardar-Gejji and Jafari has been employed successfully to solve various equations of the form u = f + N (u ) (Daftardar-Gejji and Jafari in J Math Anal Appl 316(2):753–763, 2006; Daftardar-Gejji and Kumar in Front Fract Calc 1:233, 2018). In the present paper, we introduce a new algorithm for DGJ method. The proposed algorithm is faster and very simple as compared to the existing one. To exhibit its applicability and efficiency we solve numerous non-linear equations. Keywords Caputo derivative · Riemann-Liouville integral · Decomposition methods · Convergence analysis Introduction The functional equation of the following form: u = f + N (u ), (1) where f is a known function and N , a nonlinear operator, comprises a large class of dif- ferential/ non-differential equations. In the literature, various decomposition methods are available to solve these equations such as Adomian decomposition method (ADM) [3], Homo- topy perturbation method (HPM) [4], new iterative method (NIM), which is also known as Daftardar-Gejji and Jafari method (DGJ) [1] and so on. As ADM gives the analytical approx- imate solution without linearization and discretization, hence it is applied to solve various linear/non-linear equations. However, ADM has a disadvantage that it includes tedious cal- culations of Adomian polynomials. Similarly, in HPM one has to construct homotopy and choose initial conditions, which makes HPM computationally difficult. DGJ method intro- duced by Daftardar-Gejji and Jafari, is free from the tedious calculations such as Adomian B Varsha Daftardar-Gejji vsgejji@unipune.ac.in; vsgejji@gmail.com Manoj Kumar mkmath14@gmail.com Aman Jhinga jhinga.aman@gmail.com 1 Department of Mathematics, Savitribai Phule Pune University, Pune 411007, India 2 National Defence Academy, Khadakwasala, Pune 411023, India 0123456789().: V,-vol 123