Abstract
This paper presents the study of singularly perturbed differential equations of convection-diffusion type with nonlocal boundary condition. The proposed numerical scheme is a combination of the classical finite difference method for the boundary conditions and exponential fitted operator method for the differential equations at the interior points. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical examples considered. The method is shown to be first-order accuracy independent of the perturbation parameter ε .
Highlights
Perturbed differential equations are typically characterized by the presence of a small positive parameter ε multiplying some or all of the highest order terms in differential equations
This study introduces a uniformly convergent numerical method based on the exponential fitted operator method for solving singularly perturbed boundary value problems with nonlocal boundary condition
The numerical results are tabulated in terms of maximum absolute errors, numerical rate of convergence, and uniform errors and compared with the results of the previously developed numerical methods existing in the literature (Tables 2 and 4)
Summary
Perturbed differential equations are typically characterized by the presence of a small positive parameter ε multiplying some or all of the highest order terms in differential equations Such types of problems arise frequently in mathematical models of different areas of physics, chemistry, biology, engineering science, economics, and even sociology. The well-known examples are the heat transfer problem with large Peclet numbers, semiconductor theory, chemical reactor theory, reaction-diffusion process, theory of plates, optimal control, aerodynamics, seismology, oceanography, meteorology, and geophysics Solutions of such equations usually possess thin boundary or interior layers where the solutions change very rapidly, while away from the layers, the solutions behave regularly and change slowly. Motivated by papers [35, 36], we develop a uniformly convergent numerical method for solving singularly perturbed problem under consideration
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