SIAM Journal on Scientific and Statistical Computing
An inexact Newton method for nonlinear two-point boundary-value problems
Journal of Optimization Theory and Applications
Runge-Kutta Software with Defect Control four Boundary Value ODEs
SIAM Journal on Scientific Computing
A new mesh selection strategy for ODEs
Applied Numerical Mathematics
Convergence behaviour of inexact Newton methods
Mathematics of Computation
High-order finite difference schemes for the solution of second-order BVPs
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
A new mesh selection algorithm, based on conditioning, for two-point boundary value codes
Journal of Computational and Applied Mathematics
The continuous extension of the B-spline linear multistep methods for BVPs on non-uniform meshes
Applied Numerical Mathematics
A new mesh selection algorithm, based on conditioning, for two-point boundary value codes
Journal of Computational and Applied Mathematics
High-order finite difference schemes for the solution of second-order BVPs
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
Journal of Computational and Applied Mathematics
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Boundary Value Methods (BVMs) would seem to be suitable candidates for the solution of nonlinear Boundary Value Problems (BVPs). 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.