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A second-order adaptive grid method for a nonlinear singularly perturbed problem with an integral boundary condition. (English) Zbl 1462.65088

Summary: In this paper, a nonlinear singularly perturbed problem with an integral boundary condition is studied. A hybrid finite difference method based on the midpoint difference scheme and the upwind difference scheme is constructed. An adaptive grid generation algorithm is generated by equidistributing a monitor function. The convergence analysis of the hybrid difference method on the adaptive grid is derived. It is proved by theory and experiments that the scheme is second-order uniformly convergent, which improves previous results.

MSC:

65L11 Numerical solution of singularly perturbed problems involving ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
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