A relationship between the modified Euler method and e.
A remark on solving large systems of equations in function spaces
In order to save CPU-time in solving large systems of equations in function spaces we decompose the large system in subsystems and solve the subsystems by an appropriate method. We give a sufficient condition for the convergence of the corresponding procedure and apply the approach to differential algebraic systems.
A Runge-Kutta-like method with exponential correction
A Semi-Implicit Mid-Point Rule for Stiff Systems of Ordinary Differential Equations
A software package for the numerical integration of ODEs by means of high-order Taylor methods.
A spectral regularization method for a Cauchy problem of the modified Helmholtz equation.
-stabilní metody libovolně vysokého řádu
A Study of Rosenbrock-Type Methods of High Order.
A Theory for Nyström Methods.
A Uniform Scheme for the Singularly Perturbed Riccati Equation.
A variational approach to implicit ODEs and differential inclusions
An alternative approach for the analysis and the numerical approximation of ODEs, using a variational framework, is presented. It is based on the natural and elementary idea of minimizing the residual of the differential equation measured in a usual Lp norm. Typical existence results for Cauchy problems can thus be recovered, and finer sets of assumptions for existence are made explicit. We treat, in particular, the cases of an explicit ODE and a differential inclusion. This approach also allows...
A verified method for solving piecewise smooth initial value problems
In many applications, there is a need to choose mathematical models that depend on non-smooth functions. The task of simulation becomes especially difficult if such functions appear on the right-hand side of an initial value problem. Moreover, solution processes from usual numerics are sensitive to roundoff errors so that verified analysis might be more useful if a guarantee of correctness is required or if the system model is influenced by uncertainty. In this paper, we provide a short overview...
A zero-dissipative Runge-Kutta-Nyström method with minimal phase-lag.
A ()-Stable Linear Multistep Methods for Stiff IVPs in ODEs
In this paper, a class of A()-stable linear multistep formulas for stiff initial value problems (IVPs) in ordinary differential equations (ODEs) is developed. The boundary locus of the methods shows that the schemes are A-stable for step number and stiffly stable for and . Some numerical results are reported to illustrate the method.
A0-Stability and Stiff Stability of Brown's Multistep Multiderivative Methods.
About the deficient spline collocation method for particular differential and integral equations with delay.
Absolute Monotonicity of Polynomials Occurring in the Numerical Solution of Initial Value Problems.
Absolute Monotonicity of Rational Functions Occurring in the Numerical Solution of Initial Value Problems.
Accelerated Runge-Kutta methods.
Acceleration of implicit schemes for large systems of nonlinear ODEs.