An approximate solution of singularly perturbed problem on uniform mesh

In this study, we obtain approximate solution for singularly perturbed problem of differential equation having two integral boundary conditions. With this purpose, we propose a new finite difference scheme. First, we construct this exponentially difference scheme on a uniform mesh using the finite difference method. We use the quasilinearization method and the interpolating quadrature formulas to establish the numerical scheme. Then, as a result of the error analysis, we show that the method under study is convergent in the first order. Consequently, theoretical findings are supported by numerical results obtained with an example. Approximate solutions curves are compared on the chart to provide concrete indication. The maximum errors and convergence rates obtained are given on the table for different varepsilon  and N values.