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.
Antony Prince, P. , Govindarao, L. and Elango, S. (2025). A Non-standard Finite Difference Method for Convection-diffusion Singularly Perturbed Integro-differential Equations. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.65288.2991
MLA
Antony Prince, P. , , Govindarao, L. , and Elango, S. . "A Non-standard Finite Difference Method for Convection-diffusion Singularly Perturbed Integro-differential Equations", Computational Methods for Differential Equations, , , 2025, -. doi: 10.22034/cmde.2025.65288.2991
HARVARD
Antony Prince, P., Govindarao, L., Elango, S. (2025). 'A Non-standard Finite Difference Method for Convection-diffusion Singularly Perturbed Integro-differential Equations', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.65288.2991
CHICAGO
P. Antony Prince , L. Govindarao and S. Elango, "A Non-standard Finite Difference Method for Convection-diffusion Singularly Perturbed Integro-differential Equations," Computational Methods for Differential Equations, (2025): -, doi: 10.22034/cmde.2025.65288.2991
VANCOUVER
Antony Prince, P., Govindarao, L., Elango, S. A Non-standard Finite Difference Method for Convection-diffusion Singularly Perturbed Integro-differential Equations. Computational Methods for Differential Equations, 2025; (): -. doi: 10.22034/cmde.2025.65288.2991
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