<p>In this paper, a system of singularly perturbed turning point problems with integral boundary conditions (IBCs) was considered. Due to the turning point, the problem has two boundary layers at both endpoints of the domain. To find an approximate solution to the given problem, we proposed two numerical methods, namely the Finite Difference Method (FDM) and the Cubic B-Spline Collocation Method (CBSCM). Shishkin mesh was used to construct layer-adapted piecewise uniform meshes. The integral boundary condition was discretized using Trapezoidal rule for both numerical methods. Discrete maximum norm was used to estimate the error values for both the methods. The proposed numerical methods were almost first and second-order convergence, respectively. Numerical examples were given to validate the theoretical results.</p>

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Comparison of numerical approximations for a system of second-order singularly perturbed turning point problems with integral boundary conditions

  • N. Geetha,
  • V. Raja,
  • A. Puvaneswari

摘要

In this paper, a system of singularly perturbed turning point problems with integral boundary conditions (IBCs) was considered. Due to the turning point, the problem has two boundary layers at both endpoints of the domain. To find an approximate solution to the given problem, we proposed two numerical methods, namely the Finite Difference Method (FDM) and the Cubic B-Spline Collocation Method (CBSCM). Shishkin mesh was used to construct layer-adapted piecewise uniform meshes. The integral boundary condition was discretized using Trapezoidal rule for both numerical methods. Discrete maximum norm was used to estimate the error values for both the methods. The proposed numerical methods were almost first and second-order convergence, respectively. Numerical examples were given to validate the theoretical results.