Numerical Methods for Solving Two-Point Boundary Value Problems

The numerical approximation of solutions of ordinarydifferential equations played an important role inNumerical Analysis and still continues to be anactive field of research. In this book we are mainlyconcerned with the numerical solution of thefirst-order system of nonlinear two-point boundaryvalue problems. We will focus on the problem ofsolving singular perturbation problems since this hasfor many years been a source of difficulty to appliedmathematicians engineers and numerical analystsalike. Firstly we consider deferred correctionschemes based on Mono-Implicit Runge-Kutta (MIRK) andLobatto formulae. As is to be expected the schemebased on Lobatto formulae which are implicit ismore stable than the scheme based on MIRK formulaewhich are explicit. Secondly we construct high orderinterpolants to provide the continuous extension ofthe discrete solution. It will consider theconstruction of both explicit and implicitinterpolants. The estimation of conditioning numbersis also discussed and used to develop mesh selectionalgorithms which will be appropriate for solvingstiff linear and nonlinear boundary value problems.