Abstract
This chapter discusses some recent results on multipoint boundary value problems for higher-order differential equations. The problem of best constants in Hermite interpolation is also discussed in the chapter, along with a theorem on existence and uniqueness. The chapter further explains a condition by which a function can be said to be of Lischitz class. The convergence of Picard's iterative method and the convergence of approximate Picard's iterative method is further elaborated in the chapter. The chapter also presents a discussion on the convergence of approximate quasilinearization methods, problem of best Lipschitz constants, convergence of the quasilinearization method, and continuous dependence on boundary data.
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