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High-Precision Method for Space-Time-Fractional Klein-Gordon Equation Read chapter Read first chapter

2024 | OriginalPaper | Chapter

One-Dimensional Inverse Stefan Problem Numerical Approximation Utilizing a Meshless Method

Authors : Mohammed Baati, Mohamed Louzar

Published in: Applied Mathematics and Modelling in Finance, Marketing and Economics

Publisher: Springer Nature Switzerland

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Abstract

We extend a meshless method of fundamental solutions to the one-dimensional inverse Stefan problem for the heat equation, where the boundary data is to be reconstructed on the fixed boundary. The inverse problem is ill-posed for small errors in the input measured data can cause high deviations in solution. Therefore, we incorporate Tikhonov regularization to obtain a stable solution. Numerical results are presented.

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previous chapter Fundamental Systems of Units of Some Imaginary Multiquadratic Fields of Degree 16
next chapter Comparison Between Gradient Descent and Adam Algorithms for Image Reconstruction in Diffuse Optical Tomography
Literature
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Rubinstein, L.I.: The Stefan Problem. American Mathematical Society, Providence (1971)
2.
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Cannon, J.R., Primicerio, M.: Remarks on the one-phase Stefan problem for the heat equation with the flux prescribed on the fixed boundary. Math. Anal. Appl. 35, 361–373 (1971)MathSciNetCrossRef
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Johansson, B.T., Lesnic, D., Reeve, T.: A method of fundamental solutions for the one dimensional inverse Stefan problem. Appl. Math. Modell. 35, 4367–4378 (2011)MathSciNetCrossRef
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Cannon, J.R., van der Hoek, J.: The one phase Stefan problem subject to the specification of energy. J. Math. Anal. Appl. 86, 281–291 (1982)
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Cannon, J.R., Hill, C.D.: Existence, uniqueness, stability, and monotone dependence in a Stefan problem for the heat equation. J. Math. Mech. 17, 1–19 (1967)MathSciNet
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Cannon, J.R., Primicerio, M.: Remarks on the one-phase Stefan problem for the heat equation with the flux prescribed on the fixed boundary. J. Math. Anal. Appl. 35, 361–373 (1971)MathSciNetCrossRef
Metadata
Title
One-Dimensional Inverse Stefan Problem Numerical Approximation Utilizing a Meshless Method
Authors
Mohammed Baati
Mohamed Louzar
Copyright Year
2024
Book
Applied Mathematics and Modelling in Finance, Marketing and Economics

Print ISBN: 978-3-031-42846-3

Electronic ISBN: 978-3-031-42847-0

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-42847-0_12

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