Abstract
The aim of this paper is to present finite difference method for numerical solution of singularly perturbed linear differential equation with nonlocal boundary condition. Initially, the nature of the solution of the presented problem for the numerical solution is discussed. Subsequently, the difference scheme is established on Bakhvalov-Shishkin mesh. Uniform convergence in the second-order is proven with respect to the ε− perturbation parameter in the discrete maximum norm. Finally, an example is provided to demonstrate the success of the presented numerical method. Thus, it is shown that indicated numerical results support theoretical results.
Highlights
In the present study, linear singularly perturbed problem with nonlocal boundary condition is discussed as follows: ε2u (x) + εa (x) u (x) − b(x)u(x) = f (x), u (0) = A, u(1) − γu(l1) = B, 0 < l1 < 1,0 < x < 1, where 0 < ε 0 and f (x) are assumed to be sufficientlyCopyright c 2020 The Author(s)
Different from the previous studies in the literature and for the first time, this problem is solved with the presented finite difference method on Bakhvalov-Shishkin mesh in order to demonstrate that the difference scheme has second-order convergence and a better result could be obtained
Hybrid difference schemes with variable weights on Bakhvalov-Shishkin mesh are examined to the derivative for quasi-linear singularly perturbed convection-diffusion boundary value problems in [28]
Summary
The solution of the problem (1.1)–(1.3) is within general boundary layers at x = 0 and x = 1 points Problems such as the nonlocal singular perturbation problem (1.1)–(1.3), are problems where the coefficients of the highest order derivative are a very small positive parameters such as 0 < ε
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