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Fourier, Laguerre, Laplace Transforms with applications

Aghili Arman

Journal of Mathematics and Applications

2021

Vol. 44

5--17

In this article, the author considered certain time fractional equations using joint integral transforms. Transform method is a powerful tool for solving singular integral equations, integral equation with retarded argument, evaluation of certain integrals and solution of partial fractional differential equations. The obtained results reveal that the transform method is very convenient and effective. Illustrative examples are also provided.

On the numerical solution of the initial-boundary value problem with neumann condition for the wave equation by the use of the laguerre transform and boundary elements method

Litynskyy S., Muzychuk Y., Muzychuk A.

Acta Mechanica et Automatica

2016

Vol. 10, no. 4

285--290

We consider a numerical solution of the initial-boundary value problem for the homogeneous wave equation with the Neumann condition using the retarded double layer potential. For solving an equivalent time-dependent integral equation we combine the Laguerre transform (LT) in the time domain with the boundary elements method. After LT we obtain a sequence of boundary integral equations with the same integral operator and functions in right-hand side which are determined recurrently. An error analysis for the numerical solution in accordance with the parameter of boundary discretization is performed. The proposed approach is demonstrated on the numerical solution of the model problem in unbounded three-dimensional spatial domain.