Numerical schemes for ordinary delay differential equations with random noise

Numerical Schemes for Fractional Ordinary Differential Equations

Fractional calculus, which has almost the same history as classic calculus, did not attract enough attention for a long time. However, in recent decades, fractional calculus and fractional differential equations become more and more popular because of its powerful potential applications. A large number of new differential equations (models) that involve fractional calculus are developed. These ...

Pathwise convergent higher order numerical schemes for random ordinary differential equations

Random ordinary differential equations (RODEs) are ordinary differential equations (ODEs) with a stochastic process in their vector field. They can be analysed pathwise using deterministic calculus, but since the driving stochastic process is usually only Hölder continuous in time, the vector field is not differentiable in the time variable, so traditional numerical schemes for ODEs do not achi...

Multirate Numerical Integration for Ordinary Differential Equations

Subject headings: Multirate time stepping / Local time stepping / Ordinary differential equations / Stiff differential equations / Asymptotic stability / High-order Rosenbrock methods / Partitioned Runge-Kutta methods / Mono-tonicity / TVD / Stability / Convergence. Het onderzoek dat tot dit proefschrift heeft geleid werd mede mogelijk gemaakt door een Peter Paul Peterichbeurs –verstrekt door d...

Numerical Methods for Ordinary Differential Equations

Nonstandard finite difference schemes for differential equations

In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...