Runge-Kutta methods are an important family of implicit and explicit iterative methods used for the approximation of solutions of ordinary differential equations. Explicit RungeKutta methods are unsuitable for the solution of stiff equations as their region of stability is small. Stiff equation is a differential equation for which certain numerical methods for solving the equation are numerical...

in this paper a new isolating system is introduced for short to mid-rise buildings. in comparison to conventional systems such as lrb and hrb, the proposed system has the advantage of no need to cutting edge technology and has low manufacturing cost. this system is made up of two orthogonal pairs of pillow-shaped rollers that are located between flat bed and plates. by using this system in two ...

In this paper we study numerical methods for Hybrid Fuzzy Differential equations by an appllication of the Runge-kutta Fehlberg method for fuzyy differential equations. We prove a convergence result and give numerical examples to illustrate the theory.

One of the problems in computational aeroacoustics (CAA) is the large disparity between the length and time scales of the flow field, which may be the source of aerodynamically generated noise, and the ones of the resulting acoustic field. This is the main reason why numerical schemes, used to calculate the timeand space-derivatives, should exhibit a low dispersion and dissipation error. This p...

Literature For a great deal of information on Runge-Kutta methods consult J.C. Butcher, Numerical Methods for Ordinary Differential Equations, second edition, Wiley and Sons, 2008, ISBN 9780470723357. That book also has a good introduction to linear multistep methods. In these notes we refer to this books simply as Butcher. The notes were written independently of the book which accounts for som...

In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the...

*Correspondence: [email protected] Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China Abstract Uncertain differential equations have been widely applied to many fields especially to uncertain finance. Unfortunately, we cannot always get the analytic solution of uncertain differential equations. Early researchers have put up a numerical method based on t...

We analyze explicit Runge–Kutta schemes in time combined with stabilized finite elements in space to approximate evolution problems with a first-order linear differential operator in space of Friedrichs-type. For the time discretization, we consider explicit secondand third-order Runge–Kutta schemes. We identify a general set of properties on the spatial stabilization, encompassing continuous a...

Usually the straightforward generalization of explicit Runge{Kutta methods for ordinary diierential equations to half-explicit methods for diierential-algebraic systems of index 2 results in methods of order q 2 ((8]). The construction of higher order methods is simpliied substantially by a slight modiication of the method combined with an improved strategy for the computation of the algebraic ...