The Solution of Non-Linear Equations and of Differential Equations with Two-Point Boundary Conditions

Abstract

General methods are described in this paper for the solution of sets of non-linear simultaneous equations as they arise in problems of pure and applied mathematics, where there are often more equations than unknowns (with some implicit redundancy) or more unknowns than equations (with a continuous set of solutions). The basis of the methods is the n-dimensional generalization of the Newton–Raphson process.