Applications of cubic B‐splines collocation method for solving nonlinear inverse parabolic partial differential equations. Issue 1 (18th May 2016)

• Record Type: Journal Article
• Authors: Pourgholi, Reza; Saeedi, Akram
• Is Part Of: Numerical methods for partial differential equations. Volume 33:Issue 1(2017:Jan.)
• Page Start: 88
• Page End: 104
• Publication Date: 2016-05-18
• Subjects: convergence analysis -- cubic B‐spline basis functions -- Ill‐posed inverse problems -- noisy data -- stability analysis -- tikhonov regularization method; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22073
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : In this article, we discuss a numerical method for solving some nonlinear inverse parabolic partial differential equations with Dirichlet's boundary conditions. The approach used, is based on collocation of cubic B‐splines over finite elements, so we have continuity of the dependent variable and its first two derivatives throughout the solution range. We apply cubic B‐splines for spatial variable and derivatives, which produce an ill‐posed system. We solve this system using the Tikhonov regularization method. The accuracy of the proposed method is demonstrated by applying it on two test problems. The figures and comparisons have been presented for clarity. Also the stability of this method has been discussed. The main advantage of the resulting scheme is that the algorithm is very simple, so it is very easy to implement. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 88–104, 2017