A new method based on polynomials equipped with a parameter to solve two parabolic inverse problems with a nonlocal boundary condition. Issue 5 (3rd May 2020)

• Record Type: Journal Article
• Authors: Hajishafieiha, J.; Abbasbandy, S.
• Is Part Of: Inverse problems in science and engineering. Volume 28:Issue 5(2020)
• Page Start: 739
• Page End: 753
• Publication Date: 2020-05-03
• Subjects: Inverse problem -- nonlocal boundary condition -- time-dependent diffusion coefficient -- collocation method -- source problem; 65M32 -- 35C11; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2019.1696326
• Languages: English
• ISSNs: 1741-5977

Abstract

ABSTRACT: In this paper, a new method is used based on polynomials equipped with a parameter to solve two parabolic inverse problems. These inverse problems have nonlocal boundary conditions and over-determination of data that make it difficult to solve these problems. In this method, we use the combination of the finite difference method and the finite element method. In each point t j, a nonlinear equation system is solved via the least-squares method, and then, we obtain an approximate function for the solution of the problem by using the interpolation of these points.