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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Vydané v:	Numerical algorithms Ročník 99; číslo 3; s. 1365 - 1392
Hlavní autori:	Kumar, Shashikant, Kumar, Sunil, Das, Pratibhamoy
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.07.2025 Springer Nature B.V
Predmet:	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
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Abstract	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.
AbstractList	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. 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.
Author	Kumar, Shashikant Das, Pratibhamoy Kumar, Sunil
Author_xml	– sequence: 1 givenname: Shashikant surname: Kumar fullname: Kumar, Shashikant organization: Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi – sequence: 2 givenname: Sunil surname: Kumar fullname: Kumar, Sunil email: skumar.iitd@gmail.com organization: Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi – sequence: 3 givenname: Pratibhamoy surname: Das fullname: Das, Pratibhamoy organization: Department of Mathematics, Indian Institute of Technology
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SubjectTerms	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
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Title	Second-order a priori and a posteriori error estimations for integral boundary value problems of nonlinear singularly perturbed parameterized form
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