The application of a class of one-step methods to solve the initial value problem
The Application of Rosenbrock-Wanner Type Methods with Stepsize Control in Differential-Algebraic Equations.
The best argument for the parametric continuation of solutions of differential-algebraic equations.
The Drazin inverse in multibody system dynamics.
The elimination of quantities and the solving of systems of transcendent equations by means of differential equations
The Interaction Between instability and Local Truncation Error Estimate for Predictor - Corrector Methods
The intervals of stability of Runge-Kutta methods after Richardson extrapolation
The investigation of the transient regimes in the nonlinear systems by the generalized classical method.
The method of normal splines for linear implicit differential equations of second order.
The numerical method for solving differential equations of Lane-Emden type by Padé approximation.
The numerical method of solving ordinary differential equations with the Cauchy initial condition
The numerical solution of linear time-varying DAEs with index 2 by IRK methods.
The Numerical Solution of Stiff IVPs in ODEs Using Modified Second Derivative BDF
This paper considers modified second derivative BDF (MSD-BDF) for the numerical solution of stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The methods are A-stable for step length .
The numerical treatment of stiff initial value problems
The -product approach for linear ODEs: A numerical study of the scalar case
Solving systems of non-autonomous ordinary differential equations (ODE) is a crucial and often challenging problem. Recently a new approach was introduced based on a generalization of the Volterra composition. In this work, we explain the main ideas at the core of this approach in the simpler setting of a scalar ODE. Understanding the scalar case is fundamental since the method can be straightforwardly extended to the more challenging problem of systems of ODEs. Numerical examples illustrate the...
The stability analysis of a discretized pantograph equation
The paper deals with a difference equation arising from the scalar pantograph equation via the backward Euler discretization. A case when the solution tends to zero but after reaching a certain index it loses this tendency is discussed. We analyse this problem and estimate the value of such an index. Furthermore, we show that the utilized proof technique enables us to investigate some other numerical formulae, too.
The Stability Function for Multistep Collocation Methods.
Thirteen Ways to Estimate Global Error.
Toward a two-step Runge-Kutta code for nonstiff differential systems
Various issues related to the development of a new code for nonstiff differential equations are discussed. This code is based on two-step Runge-Kutta methods of order five and stage order five. Numerical experiments are presented which demonstrate that the new code is competitive with the Matlab ode45 program for all tolerances.
Two classes of numerical methods for stiff problems