‎Solving Some Initial-Boundary Value Problems Including Non-classical ‎C‎ases of Heat Equation By Spectral and Countour Integral ‎Methods‎

In this paper, we consider some initial-boundary value problems which contain one-dimensional heat equation in non-classical case. For this problem, we can not use the classical methods such as Fourier, Laplace transformation and Fourier-Birkhoff methods. Because the eigenvalues of their spectral problems are not strictly and they are repeated or we have no eigenvalue. The presentation of the solution and also satisfying the solution in the given P.D.E and satisfing the given initial and boundary conditions are established by complex analysis theory and Countour integral method.