Richardson Extrapolation for Singularly Perturbed Fredholm Integro Differential Equations

This study numerically derived the higher order convergence for a class of singularly perturbed Fredholm integro differential equations with reaction diffusion and convection diffusion type problems. A non-standard finite difference approach is used to approximate the derivatives. The trapezoidal rule determines the integral term. The suggested numerical technique achieves a uniform convergence rate independently of the perturbation parameter. Implementing the Richardson extrapolation technique achieves a fourth order convergence rate for reaction diffusion type problems and a second order convergence rate for convection diffusion type problems. Specific numerical examples are provided to corroborate in practice the effectiveness of the theoretical findings.