Stability criteria for non-self-adjoint finite differences schemes in the subspace

The finite differences schemes with weights for the heat conduction equation with nonlocal boundary conditions u(0,t)=0u(0,t)=0, γ∂u∂x(0,t)=∂u∂x(1,t) are discussed, where γ   is a given real parameter. On some interval γ∈(γ1,γ2)γ∈(γ1,γ2) the spectrum of the differential operator contains three eigenvalues in the left complex half-plane, while the remaining eigenvalues are located in the right half-plane. Earlier only the case of one eigenvalue λ0λ0 located in the left half-plane was considered. The stability criteria of finite differences schemes is formulated in the subspace induced by stable harmonics.