Geodesic
Fitted Operator Finite Difference Method for Singularly Perturbed Differential Equations with Integral Boundary Condition
Kragujevac Journal of Mathematics, Tome 47 (2023) no. 4, p. 637 .

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This study presents a fitted operator numerical method for solving singularly perturbed boundary value problems with integral boundary condition. The stability and parameter uniform convergence of the proposed method are proved. To validate the applicability of the scheme, a model problem is considered for numerical experimentation and solved for different values of the perturbation parameter, $\varepsilon$ and mesh size, $h$. The numerical results are tabulated in terms of maximum absolute errors and rate of convergence and it is observed that the present method is more accurate and $\varepsilon$-uniformly convergent for $h\geq \varepsilon$ where the classical numerical methods fails to give good result and it also improves the results of the methods existing in the literature.
Classification : 65L11, 65L12 65L20
Keywords: fitted operator, singular perturbation, integral boundary condition 
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     author = {Habtamu Garoma Debela and Gemechis File Duressa},
     title = {Fitted {Operator} {Finite} {Difference} {Method} for {Singularly} {Perturbed} {Differential} {Equations} with {Integral} {Boundary} {Condition}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {637 },
     publisher = {mathdoc},
     volume = {47},
     number = {4},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2023_47_4_a11/}
}
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Habtamu Garoma Debela; Gemechis File Duressa. Fitted Operator Finite Difference Method for Singularly Perturbed Differential Equations with Integral Boundary Condition. Kragujevac Journal of Mathematics, Tome 47 (2023) no. 4, p. 637 . http://geodesic.mathdoc.fr/item/KJM_2023_47_4_a11/