Some Aspects of Quasilinearization

Abstract

This chapter discusses some aspects of quasilinearization. It presents the principal ideas and applications associated with the notion of quasilinearization. In the chapter, a classical variational problem from the functional equation viewpoint of dynamic programming is considered. This involves the solution of two linear equations in two unknowns. This completes the computational determination of u n+1 (x). It is noticed that only the solution of initial value problems is required along with the solution of some linear algebraic equations. In applying the quasilinearization technique to higher order equations or to systems of equations, especially where high accuracy is required, problems due to the limited high-speed storage of modern computers arise. The systems of equations are treated, provided that an inequality between vectors implies relation between components. The chapter presents the derivation of some of P. Lax's theory of weak solutions of nonlinear first order partial differential equations.