Self‐adjoint singularly perturbed boundary value problems: an adaptive variational approach

This study is intended to provide a modified variational algorithm for the numerical solution of a class of self-adjoint singularly perturbed boundary value problem, which is equally applicable to other classes of problems. The principle of the method lies in the introduction of a mixed piecewise domain decomposition and manipulating the variational iterative approach for tackling this class of problems. The uniform convergence of the technique to the exact solution is demonstrated. Numerical results, computational comparisons, suitable error measures and illustrations are provided to testify efficiently and demonstrate the convergence, efficiency and applicability of the method. Copyright © 2012 John Wiley & Sons, Ltd.