An eye surgery corneal nonlinear model: mathematical analysis and simulation via Dickson polynomials series

Abstract The paper offers an extensive mathematical study and simulation of a nonlinear corneal model pertinent to eye surgery, designed to tackle the intricacies of corneal behavior under diverse surgical situations. We utilize the Dickson polynomial series as a fundamental tool and use the benefits of the Dickson operational matrices collocation approach to establish a resilient solution framework. This method not only streamlines the computational procedure but also improves the precision of outcomes. Utilizing Dickson polynomials in our corneal nonlinear model represents a substantial advancement compared to conventional computational methods. Their unique properties provide a robust framework for accurately capturing the complex behaviors of the cornea during surgery. This results in enhanced computational efficiency, improved accuracy, and faster convergence rates compared to conventional techniques. The convergence analysis shown here illustrates the efficacy of our approach while verifying its speedy convergence to the accurate solution. Additionally, we present a comparative analysis with relevant computational techniques, demonstrating that our suggested approach delivers enhanced accuracy and efficiency. The results highlight the promise of the Dickson polynomial series in enhancing computational models in ophthalmology, facilitating future study and applications in eye surgical contexts.