Enhancing mathematical simulation: a novel integro spline quasi-interpolation for nonlocal dynamical systems

In this research, we present a novel and computationally streamlined method to tackle nonlocal initial value problems through a combination of modeling and simulation. Our approach utilizes the Integro spline quasi-interpolation technique, renowned for its effectiveness in approximating nonlocal integrals. To validate the efficacy of our proposed method, we conduct comprehensive comparisons with alternative approaches found in the existing literature for integrating nonlocal functions. Additionally, we successfully apply our suggested approach to address nonlocal Riccati, resistor-inductor circuit, and Airy oscillator dynamical systems. The numerical results obtained from these applications convincingly demonstrate the advantages and effectiveness of our developed approach in enhancing mathematical simulation.