document: Numerical approximation of nonlinear BVPs by means of BVMs Boundary Value Methods -LRB- BVMs -RRB- would seem to be suitable candidates for the solution of nonlinear Boundary Value Problems -LRB- BVPs -RRB- . They have been successfully used for solving linear BVPs together with a mesh selection strategy based on the conditioning of the linear systems . Our aim is to extend this approach so as to use them for the numerical approximation of nonlinear problems . For this reason , we consider the quasi-linearization technique that is an application of the Newton method to the nonlinear differential equation . Consequently , each iteration requires the solution of a linear BVP . In order to guarantee the convergence to the solution of the continuous nonlinear problem , it is necessary to determine how accurately the linear BVPs must be solved . For this goal , suitable stopping criteria on the residual and on the error for each linear BVP are given . Numerical experiments on stiff problems give rather satisfactory results , showing that the experimental code , called TOM , that uses a class of BVMs and the quasi-linearization technique , may be competitive with well known solvers for BVPs
doc_bio_tags: B I O O O O O O B B I I O B O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O
extractive_keyphrases: numerical approximation nonlinear boundary value problems boundary value methods mesh selection strategy newton method nonlinear differential equation stopping criteria stiff problems bvms
abstractive_keyphrases: quasi-linearization technique