Dr. Osborne is internationally recognized as a leading research worker in the field of numerical analysis having produced a steady stream of original research of high quality in three major areas, the numerical solution of boundary value problems, minimum norm problems in approximation and mathematical programming. He has successfully developed general numerical techniques for solving systems of first order differential equations and separable partial differential equations in two independent variables. His work on numerical techniques for approximating functions defined by difference equations and on penalty and barrier function algorithms form a significant contribution to approximation and optimisation theory.