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Approximate analytical solution to the Cattaneo heat conduction model with various laser sources

Nuruddeen Rahmatullah Ibrahim

Journal of Applied Mathematics and Computational Mechanics

2022

Vol. 21, nr 1

67--78

The present manuscript investigates the role being played by various laser short heating sources in a conduction process of a metallic substrate. The Cattaneo heat conduction model is considered in favour of its finiteness of conduction speed. The analytical solutions for the temperature fields are determined via the application of the Laplace integral transform. Finally, we sought a numerical Laplace inversion scheme where the analytical inversion failed and graphically examined the significance of the heating parameters on the temperature fields.

Spline regularization of numerical inversion of Mellin transform

Iqbal M.

Foundations of Computing and Decision Sciences

2000

Vol. 25, No. 1

49-64

There is described a method for inverting the Mellin transform. In the method there are applied the expansion in Laguerre polynomials, the conversion to the Laplace transformation and a convolution integral equation. The quality of the method is testified for ill-posed problems considered in the literature.