In this paper, we introduce an efficient method for solving the quadratic RICCATI differential EQUATION. In this technique, combination of Laplace trans-form and new homotopy perturbation methods (LTNHPM) are considered as an algorithm to the exact solution of the nonlinear RICCATI EQUATION. Un-like the previous approach for this problem, so-called NHPM, the present method, does not need the initial approximation to be defined as a power series. Four examples in different cases are given to demonstrate simplicity and efficiency of the proposed method.

In this paper, a fractal modification of the RICCATI differential EQUATION is presented, and the two-scale transform method combined with Taylor series is used to solve the EQUATION. Two examples are given to verify the correctness and effectiveness of the proposed method.

In this study, the asymptotic Adomian decomposition method (AADM) is imple-mented to solve fractional order RICCATI di, erential EQUATIONs. The product integra-tion method is used to solve the singular integrals, resulted from fractional derivative. Some fractional order RICCATI di, erential EQUATIONs are presented as examples to il-lustrate the ability and e, ciency of the proposed approach. The approximate solu-tions of AADM are compared with the results of the Laplace Adomian Pade method (LAPM). Generalizing AADM for solving fractional RICCATI di, erential EQUATIONs by the far-, eld approximation indicates the novelty of the paper.

In this paper, a novel hybrid method based on neural network is proposed to solve quadratic differential EQUATION. Here neural network is considered as a part of large field called neural computing or soft computing. The model finds the approximated solution of RICCATI differential EQUATION inside its domain for the close enough neighborhood of the initial point. This method, in comparison with existing numerical methods, shows that the use of neural networks provides solutions with good generalization and high accuracy.