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Self-adjoint singularly perturbed boundary value problems: an adaptive variational approach. (English) Zbl 1290.65064
A modified variational algorithm for the numerical solution of self-adjoint singularly perturbed boundary value problems is presented. The algorithm is based on a mixed piecewise domain decomposition and a certain manipulation of the variational iterative approach. Uniform convergence to the exact solution is proved and numerical results are given.

MSC:
65L11 Numerical solution of singularly perturbed problems involving ordinary differential equations
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
65L20 Stability and convergence of numerical methods for ordinary differential equations
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