An Attractive Analytic-Numeric Approach for the Solutions of Uncertain Riccati Differential Equations using Residual Power Series

In this paper, the analytic-approximate solution for a class of quadratic Riccati differential equation under uncertainty is obtained using a modified residual power series (RPS) expansion algorithm. The proposed method is a well-known efficient precise algorithm to address numerous issues in physics and engineering. The RPS is a systematic tool based on the use of the Taylor approach and residual error concept by minimizing error functions to determine the values of the coefficients of the PS according to given initial data of symmetric triangular fuzzy numbers. To interpret the solutions of fuzzy quadratic Riccati equations, the strongly-generalized differentiability sense is implemented. This algorithm provides an approximate series of solutions within a radius suitable for the desired domain. Numerical applications are introduced to clarify the compatibility and reliability of the RPS algorithm. The gained results confirm that the suggested simulated is highly reliable, simple and can be implemented to other classes of nonlinear uncertain natural problems.