Open AccessExact Analytical Solutions of Linear Dissipative Wave Equations via Laplace Transform Method
Author(s) -
Muhammad Jamil,
Rahmat Ali Khan,
Kamal Shah
Publication year - 2021
Publication title -
the punjab university journal of mathematics
Language(s) - English
Resource type - Journals
ISSN - 1016-2526
DOI - 10.52280/pujm.2021.530605
Subject(s) - laplace transform , laplace transform applied to differential equations , two sided laplace transform , inverse laplace transform , mathematical analysis , dissipative system , mathematics , partial differential equation , green's function for the three variable laplace equation , mellin transform , boundary value problem , exact solutions in general relativity , laplace's equation , laplace–stieltjes transform , physics , fourier transform , fractional fourier transform , fourier analysis , quantum mechanics
A wave phenomena evolved day after day, as various conceptsregarding waves appeared with the passage of time. These phenomenaare generally modelled mathematically by partial differential equations(PDEs). In this research, we investigate the exact analytical solutionsof one and two dimensional linear dissipative wave equations which aremodelled by second order PDEs with use of some initial and boundaryconditions. We use double Laplace transform (DLT) and triple Laplacetransform (TLT) methods to determine these exact analytical solutions.We provide examples with figures to test effectiveness of this scheme ofLaplace transform