Two classes of numerical methods for stiff problems
Two one-step methods to solve the initial value problem
Two-sided approximation to periodic solutions of ordinary differential equations.
Über die Effektivität einiger nichtlinearer Verfahren bei der numerischen Behandlung steifer Differentialgleichungssysteme (On Efficiency of some Nonlinear Methods for Numerical Solution of Stiff Differential E
Über die Koerzitivität gewöhnlicher Differenzenoperatoren und die Konvergenz von Mehrschrittverfahren.
Unconditional stability of difference formulas
The paper concerns the solution of partial differential equations of evolution type by the finite difference method. The author discusses the general assumptions on the original equation as well as its discretization, which guarantee that the difference scheme is unconditionally stable, i.e. stable without any stability condition for the time-step. A new notion of the -acceptability of the integration formula is introduced and examples of such formulas are given. The results can be applied to ordinary...
Unconditionally Stable Explicit Methods for Parabolic Equations.
Unconditionally Stable Methods for Second Order Differential Equations.
Une méthode numérique dans le domaine de la stabilité et des bifurcations pour un système différentiel périodique avec symétries
Une remarque sur l'équation des erreurs dans la solution approximative des équations différentielles
Uniform stability of linear multistep methods in Galerkin procedures for parabolic problems.
Variable multistep methods
What do Multistep Methods Approximate?
Zero Dissipative DIRKN Pairs of Order 5(4) for Solving Special Second Order IVPs
For initial value problem (IVPs) in ordinary second order differential equations of the special form possessing oscillating solutions, diagonally implicit Runge–Kutta–Nystrom (DIRKN) formula-pairs of orders 5(4) in 5-stages are derived in this paper. The method is zero dissipative, thus it possesses a non-empty interval of periodicity. Some numerical results are presented to show the applicability of the new method compared with existing Runge–Kutta (RK) method applied to the problem reduced to...
Zero-Stability Properties of the Three-Ordinate Variable Step-size Variable Formula Methods.
Zur Struktur gewisser Konvergenzkriterien bei der numerischen Lösung von Anfangswertaufgaben.
Метод Рунге-Кутта и квадратурные формулы
Методы типа Адамса с вторыми производными
Нелинейные и квазилинейные эволюционные уравнения: существование, единственность и сравнение решений; скорость сходимости разностного метода
Об одной обратной задаче для уравнения Хилла. Численные эксперименты