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.
Über die Stabilität der Ruhelage bei Differentialgleichungen mit quasihomogenen rechten Seiten.
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 Fourth Order Difference Scheme for a Singular Perturbation Problem.
Uniform methods for semilinear problems with an attractive boundary turning point.
Uniform second-order difference method for a singularly perturbed three-point boundary value problem.
Uniform stability of linear multistep methods in Galerkin procedures for parabolic problems.
Uniformly convergent difference scheme for singularly perturbed problem of mixed type.
Uniformly convergent schemes for singularly perturbed differential equations based on collocation methods.
Uniformly enclosing discretization methods and grid generation for semilinear boundary value problems with first order terms
The paper deals with uniformly enclosing discretization methods of the first order for semilinear boundary value problems. Some fundamental properties of this discretization technique (the enclosing property, convergence, the inverse-monotonicity) are proved. A feedback grid generation principle using information from the lower and upper solutions is presented.
Uniformly enclosing discretization methods for semilinear boundary value problems
Upper and Lower Bounds for Solutions of Generalized Two-Point Boundary Value Problems.
Validation of numerical simulations of a simple immersed boundary solver for fluid flow in branching channels
This work deals with the flow of incompressible viscous fluids in a two-dimensional branching channel. Using the immersed boundary method, a new finite difference solver was developed to interpret the channel geometry. The numerical results obtained by this new solver are compared with the numerical simulations of the older finite volume method code and with the results obtained with OpenFOAM. The aim of this work is to verify whether the immersed boundary method is suitable for fluid flow in channels...