Year:2020   Volume: 2   Issue: 3   Area: Applied Physics

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Dr. Samar kadhim Ajeel Al-NASSAR

INITIAL VALUE PROBLEMS OF LINEAR HEAT EQUATION SOLVABLE BY USING CLASSICAL SYMMETRIES

In this paper, we investigated the use of classical symmetries to solve initial value problems(IVPs) for the linear heat equation w_t= w_xx. In order to slove a problem of type IVP s ,it is relied that we have to make the given condition w(x,t) |_(t=t_0=0)=G(x) need be left invariant under the one parameter Lie group of transformation that leaves the linear heat equation invariant. Under this procedure, the some initial conditions solvable by using classical symmetries, were discussed and several examples were then given

Keywords: Classical Symmetries, Linear Heat Equation, Lie Symmetry Analysis, Initial Value Problems, Left Invariant.


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