Perturbed Exponentially Fitted Collocation Method for Solving Higher Order Volterra Integro-Differential Equations

This study presents a perturbed exponentially fitted collocation method for solving higher-order integrodifferential equations. The proposed method combines the strengths of exponential fitting and collocation techniques to efficiently handle the oscillatory and exponential behaviors inherent in these equations. By incorporating perturbation terms, the method enhances accuracy and stability for stiff problems. Numerical examples are solved, it is observed that the method yielded exact solution in example 4.1 and 4.2 and achieves near-machine precision (error ∼ 10−16) at x = 1.0 compared with Bessel polynomial Approximation Method, showcasing its potential for solving complex integrodifferential equations in various applications.