A Two Point Difference Scheme of an Arbitrary Order of Accuracy for BVPS for Systems of First Order Nonlinear Odes
Abstract: We consider two-point boundary value problems for systems of first-order nonlinear ordinary differential equations. Under natural conditions we show that on an arbitrary grid there exists a unique two-point exact difference scheme (EDS), i.e., a difference scheme whose solution coincides with the projection onto the grid of the exact solution of the corresponding system of differential equations. A constructive algorithm is proposed in order to derive from the EDS a so-called truncated difference scheme of an arbitrary rank. The m-TDS represents a system of nonlinear algebraic equations with respect to the approximate values of the exact solution on the grid. Iterative methods for its numerical solution are discussed. Analytical and numerical examples are given which illustrate the theorems proved. Keywords: systems of nonlinear ordinary differential equations, difference scheme, exact difference scheme, truncated difference scheme of an arbitrary order of accuracy, fixed point iteration.
- Location
-
Deutsche Nationalbibliothek Frankfurt am Main
- Extent
-
Online-Ressource
- Language
-
Englisch
- Bibliographic citation
-
A Two Point Difference Scheme of an Arbitrary Order of Accuracy for BVPS for Systems of First Order Nonlinear Odes ; volume:4 ; number:4 ; year:2004 ; pages:464-493
Computational methods in applied mathematics ; 4, Heft 4 (2004), 464-493
- Creator
-
Makarov, V.L.
Gavrilyuk, I.P.
Kutniv, M.V.
Hermann, M.
- DOI
-
10.2478/cmam-2004-0026
- URN
-
urn:nbn:de:101:1-2410261614542.007590680597
- Rights
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
-
15.08.2025, 7:25 AM CEST
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Makarov, V.L.
- Gavrilyuk, I.P.
- Kutniv, M.V.
- Hermann, M.
Other Objects (12)
Error Estimates on Arbitrary Grids for a 2nd-order Mimetic Discretization of Boundary-value Problems for Linear Odes
Orientational Order Parameters for Arbitrary Quantum Systems
On weak Brownian motions of arbitrary order
On weak Brownian motions of arbitrary order
Error estimation of the integral tau method for fourth order overdetermined ODES
Titchmarsh-Sims-Weyl theory for complex Hamiltonian systems of arbitrary order
Existence of local solutions for differential equations with arbitrary fractional order
Eigenvalue inequalities for the buckling problem of the drifting Laplacian of arbitrary order
Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
Arbitrary order spline representation of cohomology generators for isogeometric analysis of eddy current problems
Optimising orbit counting of arbitrary order by equation selection
Existence and Uniqueness of Exact WKB Solutions for Second-Order Singularly Perturbed Linear ODEs
Error Estimates on Arbitrary Grids for a 2nd-order Mimetic Discretization of Boundary-value Problems for Linear Odes
Orientational Order Parameters for Arbitrary Quantum Systems
On weak Brownian motions of arbitrary order
On weak Brownian motions of arbitrary order
Error estimation of the integral tau method for fourth order overdetermined ODES
Titchmarsh-Sims-Weyl theory for complex Hamiltonian systems of arbitrary order
Existence of local solutions for differential equations with arbitrary fractional order
Eigenvalue inequalities for the buckling problem of the drifting Laplacian of arbitrary order
Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
Arbitrary order spline representation of cohomology generators for isogeometric analysis of eddy current problems
Optimising orbit counting of arbitrary order by equation selection
Existence and Uniqueness of Exact WKB Solutions for Second-Order Singularly Perturbed Linear ODEs
Error Estimates on Arbitrary Grids for a 2nd-order Mimetic Discretization of Boundary-value Problems for Linear Odes
Orientational Order Parameters for Arbitrary Quantum Systems
On weak Brownian motions of arbitrary order
On weak Brownian motions of arbitrary order
Error estimation of the integral tau method for fourth order overdetermined ODES
Titchmarsh-Sims-Weyl theory for complex Hamiltonian systems of arbitrary order
Existence of local solutions for differential equations with arbitrary fractional order
Eigenvalue inequalities for the buckling problem of the drifting Laplacian of arbitrary order
Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
Arbitrary order spline representation of cohomology generators for isogeometric analysis of eddy current problems
Optimising orbit counting of arbitrary order by equation selection