Numerical simulation of the time-delay optoelectronic oscillator model using locally supported radial basis functions

Optoelectronic oscillators are essential tools for generating pure microwave and millimeter-wavelength signals used in high-speed telecommunications, signal processing, radar, and related domains. This research investigates the numerical solution of the retarded optoelectronic oscillator model, described by delay Volterra integro-differential equations. We present a technique by employing the discrete collocation method and locally supported radial basis functions constructed on a set of scattered points. This scheme has the potential to achieve a accurate approximate solution by solving several smaller systems rather than one large system, resulting in a minimization of computational volume compared to its global counterpart. The discretization process is accomplished using the composite Gauss–Legendre quadrature formula. We estimate the error bound and convergence rate of our proposed scheme, supported by simulations that showcase the method’s reliability and efficiency. Additionally, we conducted a comparison of the computational efficiency between the offered method and its global counterpart, confirming that the introduced method is better than its global equivalent. The numerical results obtained confirm its alignment with the theoretical error estimates.