We study a model of autonomous unipolar charge injection from the cathode in poorly conductive liquid steady electric field flat horizontal capacitor. According to this model, density injected into has constant term and directly proportional strength An electrohydrodynamic approximation is used. The case weightlessness an isothermal considered. equilibrium distributions potential limiting were ...

The aim of this paper is to design a new family of numerical methods of arbitrarily high order for systems of rst-order diierential equations which are to be termed pseudo two-step Runge-Kutta methods. By using collocation techniques, we can obtain an arbitrarily high-order stable pseudo two-step Runge-Kutta method with any desired number of implicit stages in retaining the two-step nature. In ...

Systems of functional-diierential and functional equations occur in many biological, control and physics problems. They also include functional diierential equations of neutral type as special cases. In this paper we present a numerical method that is based on the continuous extension of the Runge{Kutta method (for ordinary diierential equations) and the collocation method (for functional equat...

We present a new class of adaptivity algorithms for time-dependent partial differential equations (PDE) that combines adaptive higher-order finite elements (hp-FEM) in space with arbitrary (embedded, higher-order, implicit) Runge-Kutta methods in time. Weak formulation is only created for the stationary residual of the equation, and the Runge-Kutta method is supplied via its Butcher’s table. Ar...

This paper is concerned with time-stepping numerical methods for computing sti semi-discrete systems of ordinary di erential equations for transient hypersonic ows with thermo-chemical nonequilibrium. The sti ness of the equations is mainly caused by the viscous ux terms across the boundary layers and by the source terms modeling nite-rate thermo-chemical processes. Implicit methods are needed ...

In this paper we further explore a class of high order TVD (total variation diminishing) Runge-Kutta time discretization initialized in a paper by Shu and Osher, suitable for solving hyperbolic conservation laws with stable spatial discretizations. We illustrate with numerical examples that non-TVD but linearly stable Runge-Kutta time discretization can generate oscillations even for TVD (total...

We propose an adaptive and explicit Runge–Kutta–Fehlberg method coupled with a fourth-order compact scheme to solve the American put options problem. First, free boundary problem is converted into system of partial differential equations fixed domain by using logarithm transformation taking additional derivatives. With addition intermediate function boundary, quadratic formula derived compute v...

Abstract—In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing ...

In this paper we study a class of explicit pseudo two-step Runge-Kutta (EP-TRK) methods for rst-order ODEs for parallel computers. We investigate linear stability and derive methods with enlarged stability regions. In numerical experiments on a shared memory computer we compare a parallel variable step size EPTRK implementation with the eecient sequential Runge-Kutta method dopri5.