In order to formulate the solution of parabolic problem (1) by using the Fourier method of separation of variables, let us first introduce an auxiliary function (v x,t)) as follows: v x,t)=u x,t -psi_{0}(t)-psi_{1}(t)x,t -psi_{[0}1], by which we t -psi_{m problem (1) int -psi_{blem with homogeneous boundary conditions.
In order to formulate the solution of parabolic problem (1) by using the Fourier method of the separation of variables, let us first introduce an auxiliary function v ( x, t ) as follows: v ( x, t ) = u ( x, t ) − ψ 0 ( t ) − ψ 1 ( t ) x, x ∈ [ 0, 1 ], by which we transform problem (1) into a problem with homogeneous boundary conditions.
In order to formulate the solution of parabolic problem (1) by using the Fourier method of the separation of variables, let us first introduce an auxiliary function (v x,t)) as follows: v x,t)=u x,t -psi_{1}(t)+(1-x)frac{psi_{0}(t)}{k(0)},t -psi_{n[0,1}, by which we transform problem (1) into a problem with homogeneous boundary conditions.
We analyze the solvability, stability and convergence of the proposed scheme using the Fourier method.
In Section 2, the existence and uniqueness of the solution of the inverse problem (1 -(4) is proved by using the Fourier method.
In this paper, we identify the unknown source which depends only on spatial variable for a fractional diffusion equation using the Fourier method.
Taking consideration of all the upper bounds in (11), (12), and (14), rate regions in terms of R DL, R UL, and R UL+R DL can be obtained by using the Fourier-Motzkin elimination (FME) method (see Appendix D of [43]).
Using the Fourier score based method, a protein was classified as cyclic if the Fourier score for the random protein profiles, generated using different permutations of the original profile, exceeded the Fourier score for the original expression in less than 1% of the permutations (p-value <1%) [11].
The continuous model is reduced to a finite degree of freedom system using the Galerkin method and a Fourier Bessel approach.
The mode shapes are expanded in a Fourier Bessel series by using the Rayleigh Ritz method.
The temperature fields for both Fourier and non-Fourier heat conduction models have been calculated using the finite difference method by assuming a convective boundary condition at the location of the fluid-carrying tube attached to the absorber plate.
