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Applications of cubic B‐splines collocation method for solving nonlinear inverse parabolic partial differential equations
Author(s) -
Pourgholi Reza,
Saeedi Akram
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22073
Subject(s) - mathematics , collocation method , tikhonov regularization , partial derivative , partial differential equation , mathematical analysis , nonlinear system , dirichlet boundary condition , inverse problem , parabolic partial differential equation , boundary value problem , boundary (topology) , regularization (linguistics) , differential equation , ordinary differential equation , computer science , physics , quantum mechanics , artificial intelligence
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