On Stability Analysis of Finite-Difference Schemes for Some Parabolic Problems with Nonlocal Boundary Conditions

Abstract

In this article, one-dimensional parabolic and pseudo-parabolic equations with nonlocal boundary conditions are approximated by the implicit Euler finite-difference scheme. For a parabolic problem, the stability analysis is done in the weak H ⁻¹ type norm, which enables us to generalize results obtained in stronger norms. In the case of a pseudo-parabolic problem, the stability analysis is done in the discrete analog of the norm. It is shown that a solution of the proposed finite-discrete scheme satisfies stronger stability estimates than a discrete solution of the parabolic problem. Results of numerical experiments are presented.

Keywords:

• Convergence analysis
• Finite-difference method
• Nonlocal boundary conditions
• Parabolic problem
• Pseudo-parabolic problem
• Stability

Mathematics Subject Classification:

• 65M06
• 65M12

ACKNOWLEDGMENTS

The authors would like to thank the referee for his constructive criticism which helped to improve the clarity and quality of this paper.

Notes

Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lnfa.