Computational Method for Singularly Perturbed Differential-Difference Equation via Mixed Non-Polynomial Quadratic Spline Approach

Resumo

In this paper, a mixed nonpolynomial quadratic spline technique is implemented using three nodal points for solving singularly perturbed differential-difference equation which is reduced to an equivalent two point singularly perturbed boundary value problem. A fitting factor is incorporated in the second order finite difference scheme which handles the oscillations that arising in the boundary layer. The discrete system obtained from the difference scheme is solved by employing Thomas algorithm. A brief convergence analysis is demonstrating that the suggested approach achieves fourth-order convergence. Numerous illustrations are provided to highlight the efficiency of the suggested approach. Comparative analysis is made to validate the accuracy and reliability of the proposed strategy.