TY - JOUR
T1 - Modulating functions-based method for parameters and source estimation in one-dimensional partial differential equations
AU - Asiri, Sharefa M.
AU - Laleg-Kirati, Taous-Meriem
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Research reported in this publication was supported by King Abdullah University of Science and Technology (KAUST).
PY - 2016/10/20
Y1 - 2016/10/20
N2 - In this paper, modulating functions-based method is proposed for estimating space–time-dependent unknowns in one-dimensional partial differential equations. The proposed method simplifies the problem into a system of algebraic equations linear in unknown parameters. The well-posedness of the modulating functions-based solution is proved. The wave and the fifth-order KdV equations are used as examples to show the effectiveness of the proposed method in both noise-free and noisy cases.
AB - In this paper, modulating functions-based method is proposed for estimating space–time-dependent unknowns in one-dimensional partial differential equations. The proposed method simplifies the problem into a system of algebraic equations linear in unknown parameters. The well-posedness of the modulating functions-based solution is proved. The wave and the fifth-order KdV equations are used as examples to show the effectiveness of the proposed method in both noise-free and noisy cases.
UR - http://hdl.handle.net/10754/622431
UR - http://www.tandfonline.com/doi/full/10.1080/17415977.2016.1240793
UR - http://www.scopus.com/inward/record.url?scp=84992061452&partnerID=8YFLogxK
U2 - 10.1080/17415977.2016.1240793
DO - 10.1080/17415977.2016.1240793
M3 - Article
SN - 1741-5977
VL - 25
SP - 1191
EP - 1215
JO - Inverse Problems in Science and Engineering
JF - Inverse Problems in Science and Engineering
IS - 8
ER -