Journal
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
Volume 27, Issue 11, Pages 1498-1520Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/17415977.2018.1481405
Keywords
Haar wavelets; inverse heat problems; collocation method; partial differential equation; space-dependent heat source
Ask authors/readers for more resources
In this paper, two different Haar wavelet collocation multi-resolution procedures are proposed for linear partial differential equations (PDEs) with an unknown space-dependent heat source and an unknown solution. An appropriate transformation is used to convert a non-homogeneous PDE into a homogeneous form. Two techniques based on multi-resolution Haar wavelets collocation methods are proposed for numerical evaluation of the unknown space-dependent heat source. In homogeneous form, first-order finite-difference approximation is used to discretize the time derivative and finite Haar wavelets series is used for approximation of the space derivatives. Unlike other numerical methods, the proposed methods have well-conditioned Haar coefficient matrices and need not be supplemented by any regularization technique. Several numerical experiments are carried out to validate accuracy, simple applicability and well-conditioned behaviour of the Haar system coefficient matrices of the proposed algorithms.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available