On the solution of a differential equation occurring in the problem of heat convection in laminar flow through a tube with slip-flow.
One-step methods for ordinary differential equations with parameters
In the present paper we are concerned with the problem of numerical solution of ordinary differential equations with parameters. Our method is based on a one-step procedure for IDEs combined with an iterative process. Simple sufficient conditions for the convergence of this method are obtained. Estimations of errors and some numerical examples are given.
Pointwise Lower and Upper Bounds for Eigenfunctions of Ordinary Differential Operators.
Postprocessing and higher order convergence for the mixed finite element approximations of the Stokes eigenvalue problems
In this paper we propose a method for improving the convergence rate of the mixed finite element approximations for the Stokes eigenvalue problem. It is based on a postprocessing strategy that consists of solving an additional Stokes source problem on an augmented mixed finite element space which can be constructed either by refining the mesh or by using the same mesh but increasing the order of the mixed finite element space.
Small Potential Corrections for the Discrete Eigenvalues of the Sturm-Liouville Problem.
Solving heat and wave-like equations using He's polynomials.
Sturm-Liouville-Problème mit schwach singulären Koeffizientenfunktionen. Teil I. Eigenwertproblem.
The Approximation of Generalized Turning Points by Projection Methods with Superconvergence to the Critical Parameter.
The numerical treatment of perturbed bifurcation in boundary value problems
The virtual element method for eigenvalue problems with potential terms on polytopic meshes
We extend the conforming virtual element method (VEM) to the numerical resolution of eigenvalue problems with potential terms on a polytopic mesh. An important application is that of the Schrödinger equation with a pseudopotential term. This model is a fundamental element in the numerical resolution of more complex problems from the Density Functional Theory. The VEM is based on the construction of the discrete bilinear forms of the variational formulation through certain polynomial projection operators...
Two new finite difference methods for computing eigenvalues of a fourth order linear boundary value problem.
Вариационно-сеточная аппроксимация
К вопросу об аппроксимации функций собственными решениями двух задач Штурма-Лиувилля.
К теории вырожденных систем обыкновенных дифференциальных уравнений.