Second-order a priori and a posteriori error estimations for integral boundary value problems of nonlinear singularly perturbed parameterized form

In this work, we present the a priori and a posteriori error analysis of a hybrid difference scheme for integral boundary value problems of nonlinear singularly perturbed parameterized form. The discretization for the nonlinear parameterized equation constitutes a hybrid difference scheme which is b...

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Bibliographic Details
Published in:Numerical algorithms Vol. 99; no. 3; pp. 1365 - 1392
Main Authors: Kumar, Shashikant, Kumar, Sunil, Das, Pratibhamoy
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2025
Springer Nature B.V
Subjects:
Algebra
Algorithms
Approximation
Boundary conditions
Boundary value problems
Chemical reactions
Computer Science
Discretization
Error analysis
Numeric Computing
Numerical Analysis
Parameterization
Singular perturbation
Theory of Computation
Singularly perturbed problems
Parameterized problems
Hybrid difference scheme
Nonlinear problems
Integral boundary conditions
Layer-adapted meshes
Nonlocal problems
65L70
65L20
65L50
65L12
meshes
65L11
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:In this work, we present the a priori and a posteriori error analysis of a hybrid difference scheme for integral boundary value problems of nonlinear singularly perturbed parameterized form. The discretization for the nonlinear parameterized equation constitutes a hybrid difference scheme which is based on a suitable combination of the trapezoidal scheme and the backward difference scheme. Further, we employ the composite trapezoidal scheme for the discretization of the nonlocal boundary condition. A priori error estimation is provided for the proposed hybrid scheme, which leads to second-order uniform convergence on various a priori defined meshes. Moreover, a detailed a posteriori error analysis is carried out for the present hybrid scheme which provides a proper discretization of the error equidistribution at each partition. Numerical results strongly validate the theoretical findings for nonlinear problems with integral boundary conditions.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-024-01918-5