DOI: 10.12732/ijam.v38i2.4
A RADIAL BASIS FUNCTION -
FINITE DIFFERENCE APPROACH FOR
TIME-DEPENDENT PARAMETER IDENTIFICATION
OF THE HEAT EQUATION
Nadun Kulasekera Mudiyanselage 1,§,
Dulashini Karunarathna 2
1 Mount St Mary’s University
Department of Mathematics and Computer Science
Emmitsburg, Maryland, USA
2 University of Peradeniya
Postgraduate Institute of Science
Peradeniya, SRI LANKA
Abstract. This manuscript focuses on solving inverse problems that approximate the time-dependent heat conductivity coefficients and the solutions of parabolic partial differential equations. Solving these problems poses significant challenges due to their ill-posed nature, as the solutions may not depend continuously on the input data, particularly in the presence of noise. As a result, it is crucial to design stable and reliable numerical methods. This paper introduces a new, straightforward, and effective framework based on the Radial Basis Function - Finite Difference
(RBF-FD) method to address inverse time-dependent parameter identification problems in parabolic partial differential equations. The RBF-FD method offers a computationally efficient higher-order approach to tackle these problems, overcoming some common limitations of existing
numerical methods, such as instability, high computational demands, and reduced accuracy.
How
to cite this paper?
DOI: 10.12732/ijam.v38i2.4
Source: International Journal of
Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2025
Volume: 38
Issue: 2
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