An inexact monotone method for solving semilinear parabolic problems

Boglaev, Igor

doi:10.1016/j.amc.2012.09.067

Cited by 3 publications

(3 citation statements)

References 6 publications

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“…In recent years, the researchers have made efforts to provide consistent numerical techniques to solve NSPPPDEs. In [4] Igor Boglaev presented a monotone iterative algorithm for nonlinear singularly perturbed parabolic problem and then in [5] Igor Boglaev presented an inexact monotone iterative method based on method of upper and lower solution for a class of semi-linear parabolic singularly perturbed problem. In [18,19] Kopteva and Linß used an elliptic reconstruction approach and provide the error estimate in maximum norm using Green's function.…”

Section: Introductionmentioning

confidence: 99%

An Iterative Analytic Approximation for a Class of Non-Linear Singularly Perturbed Parabolic Partial

Khari

Kumar

2022

Preprint

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In this article, a closed-form iterative analytic approximation to a class of nonlinear singularly perturbed parabolic partial differential equation is developed and analysed for convergence. We have considered both parabolic reaction diffusion and parabolic convection diffusion type of problems in this paper. The solution of this class of problem is polluted by a small dissipative parameter, due to which solution often shows boundary and interior layers. A sequence of approximate analytic solution for the above class of problems is constructed using Lagrange multiplier approach. Within a general frame work, the Lagrange multiplier is optimally obtained using variational theory and Liouville-Green’s transformation. The sequence of approximate analytic solutions so obtained is proved to converge the exact solution of the problem. To demonstrate the proposed method’s efficiency and accuracy, two linear and one nonlinear test problem have been taken into account.

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Section: Introductionmentioning

confidence: 99%

An Iterative Analytic Approximation for a Class of Non-Linear Singularly Perturbed Parabolic Partial

Khari

Kumar

2022

Preprint

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“…For the approximation of the differential operator, we use the central difference approximations on the five-point square stencil with N 1 = N 2 = N , which satisfies (4). A lower solution is defined by U In Table 1, for various values of N, we give convergence iteration counts.…”

Section: C78mentioning

confidence: 99%

“…Boglaev [4] constructed and investigated inexact monotone methods for solving semilinear parabolic problems. The aim of this article is to construct inexact monotone methods for solving semilinear elliptic problems, where the outer iterations are based on the monotone method discussed by Boglaev [2] and the inner iterations are based on the Jacobi and Gauss-Seidel iterative methods.…”

Section: Introductionmentioning

confidence: 99%

Inexact monotone methods for solving nonlinear elliptic problems

Boglaev

2015

ANZIAMJ

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We numerically solving semilinear elliptic problems with the method of upper and lower solutions. Inexact monotone iterative methods are constructed, where monotone linear systems are solved by the Jacobi or Gauss-Seidel methods only approximately. The inexact monotone methods combine the quadratic monotone iterative method at outer iterations and the Jacobi or Gauss-Seidel methods at inner iterations, and possess global monotone convergence. Results of numerical experiments are presented.

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An inexact monotone method for solving semilinear parabolic problems

Cited by 3 publications

References 6 publications

An Iterative Analytic Approximation for a Class of Non-Linear Singularly Perturbed Parabolic Partial

An Iterative Analytic Approximation for a Class of Non-Linear Singularly Perturbed Parabolic Partial

Inexact monotone methods for solving nonlinear elliptic problems

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