Parallel algorithms for initial and boundary value problems for linear ordinary differential equations and their systems
Practical method for solving differential equations and their systems bu means of Taylor series
Quadratic and homogeneous Hamilton-Poisson systems on .
Recent progress in the integration of Poisson systems via the mid-point rule and Runge-Kutta algorithm.
Reducibility and characterization of symplectic Runge-Kutta methods.
Reliable numerical modelling of malaria propagation
We investigate biological processes, particularly the propagation of malaria. Both the continuous and the numerical models on some fixed mesh should preserve the basic qualitative properties of the original phenomenon. Our main goal is to give the conditions for the discrete (numerical) models of the malaria phenomena under which they possess some given qualitative property, namely, to be between zero and one. The conditions which guarantee this requirement are related to the time-discretization...
Richardson Extrapolation combined with the sequential splitting procedure and the θ-method
Initial value problems for systems of ordinary differential equations (ODEs) are solved numerically by using a combination of (a) the θ-method, (b) the sequential splitting procedure and (c) Richardson Extrapolation. Stability results for the combined numerical method are proved. It is shown, by using numerical experiments, that if the combined numerical method is stable, then it behaves as a second-order method.
Runge-Kutta methods for parabolic equations with nonsmooth initial data
Solution of the porous media equation by a compact finite difference method.
Solving ordinary differential equation systems by approximation in a graphical way.
Solving the systems of equations arising in the discretization of some nonlinear p.d.e.'s by implicit Runge-Kutta methods
Stability analysis of numerical methods for delay differential equations.
Stability, Boundedness and Existenceof Periodic Solutions to Certain Third Order Nonlinear Differential Equations
In this paper, criteria are established for uniform stability, uniform ultimate boundedness and existence of periodic solutions for third order nonlinear ordinary differential equations. In the investigation Lyapunov’s second method is used by constructing a complete Lyapunov function to obtain our results. The results obtained in this investigation complement and extend many existing results in the literature.
Stability of the method of lines.
Stabilization of Cowell's Method.
The CUDA implementation of the method of lines for the curvature dependent flows
We study the use of a GPU for the numerical approximation of the curvature dependent flows of graphs - the mean-curvature flow and the Willmore flow. Both problems are often applied in image processing where fast solvers are required. We approximate these problems using the complementary finite volume method combined with the method of lines. We obtain a system of ordinary differential equations which we solve by the Runge-Kutta-Merson solver. It is a robust solver with an automatic choice of the...
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 Stability Function for Multistep Collocation Methods.
Time discretization of parabolic boundary integral equations.