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**A computational method for solving third-order singularly perturbed boundary-value problems.**
*(English)*
Zbl 1138.65060

Summary: A new computational method is presented for solving a class of third-order singularly perturbed boundary-value problems with a boundary layer at the left of the underlying interval. In this method, first the given third-order singularly perturbed boundary-value problem is transformed into a system of two ordinary differential equations subject to suitable initial and boundary conditions and a zeroth-order asymptotic expansion for the solution of the given problem is constructed. Then the reduced terminal value problem is solved analytically in the reproducing kernel space.

This method is effective and easy to implement. A numerical example is studied to demonstrate the accuracy of the present method. Results obtained by the method are found to be in good agreement with the exact solution not only in the boundary layer, but also away from the layer.

This method is effective and easy to implement. A numerical example is studied to demonstrate the accuracy of the present method. Results obtained by the method are found to be in good agreement with the exact solution not only in the boundary layer, but also away from the layer.

### MSC:

65L10 | Numerical solution of boundary value problems involving ordinary differential equations |

34B05 | Linear boundary value problems for ordinary differential equations |

34E15 | Singular perturbations for ordinary differential equations |

### Keywords:

analytical solution; asymptotic expansion; reproducing kernel space; singular perturbation; boundary layer; numerical examples
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\textit{M. Cui} and \textit{F. Geng}, Appl. Math. Comput. 198, No. 2, 896--903 (2008; Zbl 1138.65060)

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### References:

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