Analytical Construction of Uniformly Convergent Method for Convection Diffusion Problem

In this paper, we study the uniformly convergent method on equidistant meshes for the convection-diffusion problem of type; where the formal adjoint operator of L. Lu=-εu''+bu'+c u=f(x), u(0)=0, u(1)=0 At the end of the this paper we will generate the scheme; -e^(ρ_i )/(e^(ρ_i )+1) U_(i-1)+U_i-1/(e^(ρ_i )+1) U_(i+1)=(f_i-c_i U_i ) h/b ((e^(ρ_i )-1)/(e^(ρ_i )+1))

On the spectra of non-selfadjoint differential operators and their adjoints in direct sum spaces

The general ordinary quasidifferential expressionMpofnth order, with complex coefficients and its formal adjointMp+on any finite number of intervalsIp=(ap,bp),p=1,…,N, are considered in the setting of the direct sums ofLwp2(ap,bp)-spaces of functions defined on each of the separate intervals. And a number of results concerning the location of the point spectra and regularity fields of general differential operators generated by such expressions are obtained.

A note on special involutions

The algebra consisting of those linear transformations of a complex inner product space that have a formal adjoint is shown to possess a special involution. Two earlier results concerning special involutions are then generalized.

ON $L^2_W$ QUASI-DERIVATIVES FOR SOLUTIONS OF PERTURBED GENERAL QUASI-DIFFERENTIAL EQUATIONS

This paper is concerned with square integrable quasi-derivatives for any solution of a general quasi-differential equations of nth order with complex coefficients $M[y] -\lambda wy = w f(t, y^{[0]}, \cdots ,y^{[n- 1]})$, $t \in [a,b)$ provided that all $r$th quasi-derivatives of solutions of $M[y] -\lambda wy = 0$ and all solutions of its formal adjoint $M^+[z] -\lambda wz = 0$ are in $L _W^2(a, b)$ and under suitable conditions on the function $f$.

Classification of regularly solvable first-order differential operators

SynopsisIn this article the expression τφ: = pφ + qφ with complex-valued coefficients is considered. We are particularly concerned with this expression when it is not formally symmetric, i.e., τ ≠ τ+, where τ+ is the formal adjoint of τ, and especially with the operators which are regularly solvable with respect to the minimal operators generated by τ and τ+ in the sense of W. D. Evans in [3]. This article is divided into five sections: Section 1 is an introduction, Section 2 is a brief study of the regular problem, in Section 3, some preliminary results in the singular case are displayed in Section 4, the joint field of regularity in the singular case is investigated and in Section 5, we discuss the case when .