A variable order finite difference method for nonlinear multipoint boundary value problems
Marianela Lentini,Victor Pereyra +1 more
TL;DR: An adaptive finite difference method for first order nonlinear systems of ordinary differential equations subject to multipoint nonlinear boundary conditions is presented and is based on a discretization studied earlier by H. B. Keller.
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Abstract: An adaptive finite difference method for first order nonlinear systems of ordinary differential equations subject to multipoint nonlinear boundary conditions is presented. The method is based on a discretization studied earlier by H. B. Keller. Variable order is provided through deferred corrections, while a built-in natural asymptotic estimator is used to automatically refine the mesh in order to achieve a required tolerance. Extensive numerical experimentation and a FORTRAN program
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A BVP solver based on residual control and the Maltab PSE
TL;DR: Theoretical and software developments resulting in bvp4c, a capable BVP solver that is exceptionally easy to use are presented.
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Computational Solution of Linear Two-Point Boundary Value Problems via Orthonormalization
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An adaptive finite difference solver for nonlinear two point boundary problems with mild boundary layers.
Marianela Lentini,Victor Pereyra +1 more
TL;DR: The combination of automatic variable order (via deferred corrections) and automatic (adaptive) mesh selection produces, as in the case of initial value problem solvers, a versatile, robust, and efficient algorithm.
PASVA3: An Adaptive Finite Difference Fortran Program for First Order Nonlinear, Ordinary Boundary Problems
Victor Pereyra
- 14 May 1978
TL;DR: H e r e the f u n c t i o n s co, f, g t a k e v a l u e s i n ]Rd; f and g a r e a s s u m e d to be s u f f i c i e n t l y s m o o t h , and the authors a l s o a s o m e t h a t p r o b l e m.
157
References
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Iterative Solution of Nonlinear Equations in Several Variables
J.M. Ortega,Werner C. Rheinboldt +1 more
- 01 Jun 1970
TL;DR: In this article, the authors present a list of basic reference books for convergence of Minimization Methods in linear algebra and linear algebra with a focus on convergence under partial ordering.
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