High-order multistep methods for boundary value problems (Q1902065)

The use of boundary value methods for the numerical solution of two-point boundary value problems is investigated. The considered methods are high- order linear multistep methods that are unstable in the classical sense. Convergence is analyzed, when the method is applied to the scalar linear problem \(y'= \lambda y\), \(b_1 y(0)+ b_2 y(T)= \eta\). A series of numerical experiments illustrate the theoretically expected convergence rate.