University of Tabriz Computational Methods for Differential Equations 2345-3982 Articles in Press 2025 10 11 A Non-standard Finite Difference Method for Convection-diffusion Singularly Perturbed Integro-differential Equations 20540 10.22034/cmde.2025.65288.2991 EN P Antony Prince Department of Mathematics, Amrita School of Physical Science, Coimbatore, Amrita Vishwa Vidyapeetham, India. L Govindarao Department of Mathematics, Amrita School of Physical Science, Coimbatore, Amrita Vishwa Vidyapeetham, India. Sekar Elango Department of Mathematics, Amrita School of Physical Science, Coimbatore, Amrita Vishwa Vidyapeetham, India. Journal Article 2025 01 03 This paper tackles singularly perturbed second-order ordinary differential equations and parabolic partial differential equations with the Fredholm integral term. A non-standard finite difference method is applied the derivative terms, the trapezoidal rule treats the integral term and the backward Euler method deals with the temporal derivative phrase. The approximate numerical technique for the second-order Fredholm integro-ordinary differential (convection-diffusion type) equations provides a convergence rate of order one. The time-dependent parabolic Fredholm integro-partial differential (convection-diffusion type) equations possess a convergence rate of order one. Specific numerical examples are provided to illustrate the effectiveness of the theoretical findings. https://cmde.tabrizu.ac.ir/article_20540_53492bee736db4c1e5a3806b48b6bd6c.pdf