Exponentially fitted methods applied to fourth-order boundary value problems

Fourth-order boundary value problems are solved by means of exponentially fitted methods of different orders. These methods, which depend on a parameter, can be constructed following a six-step flow chart of Ixaru and Vanden Berghe. Special attention is paid to the expression for the error term and to the choice of the parameter in order to make the error as small as possible. Some numerical examples are given to illustrate the practical implementation issues of these methods.

► We apply exponential fitting techniques to fourth-order boundary value problems.
► Methods of order 6, 8 and 10 are constructed and attention is paid to the explicit form of the leading error term.
► The method leads to an ill-conditioned system.
► Reformulating the problem as a system of second-order equations greatly improves the numerical results.