Cubic B-spline method for the solution of an inverse parabolic system

Abstract

In this paper, a numerical method is proposed for the numerical solution of a linear system with suitable initial and boundary conditions using the cubic B-spline collocation scheme to determine the unknown boundary condition. We apply the cubic B-spline for the spatial variable and the derivatives which, generate an ill-posed linear system of equations. In this regard, to overcome, to this drawback, we employ the Tikhonov regularization method for solving the resultant linear system. It is proved that the proposed method has the order of convergence . Also, the conditional stability using the Von-Neumann method is established under suitable assumptions. Finally, some numerical results are reported to show the efficiency and robustness of the proposed approach for solving the inverse problems.

Keywords:

• Ill-posed inverse problems
• cubic B-spline
• Tikhonov regularization method
• convergence analysis
• stability analysis
• noisy data

AMS Subject Classifications:

• 65M32
• 35G46

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the Damghan University.