Nonstandard Finite Difference Predictor Corrector Method for Quadratic Riccati Differential Equation (European Journal of Pure and Applied Mathematics, 2025)
Solving nonlinear differential equations reliably and effectively is critical for applications in epidemiology, ecology, and finance. Traditional finite difference approaches frequently exhibit numerical instability and fail to maintain crucial features such as positivity and boundedness. Motivated by these restrictions, we provide an unconditionally stable Nonstandard Finite Difference Predictor-Corrector (NSFD-PC) strategy for solving nonlinear quadratic Riccati differential equations. Particularly when the step size h rises, NSFD-PC typically yields the solution that is closer to the exact solution. Riccati differential equation is 1st-order quadratic ode with several systems and control theory applications. Our technique achieves first-order temporal precision while keeping the continuous model's fundamental qualitative properties. We compare the proposed NSFD-PC scheme to the usual Euler Predictor-Corrector approach and find that it performs much better in accuracy and consistency with exact answers. The results show that our method is a superior and dependable option for solving nonlinear differential equations, making it extremely useful in various applications.
Keywords: Non linear differential equations; Riccati problem; NSFD-PC Scheme; stability analysis