The problem associated with the stiff ordinary differential equation (ODE) systems in parallel processing is that the calculus can not be started simultaneously on many processors with an explicit formula. The proposed algorithm is constructed for a special classes of stiff ODE, those of the form y'(t)=A(t)y(t)+g(t). It has a high efficiency in the implementation on a distributed memory multipr...

Implicit-explicit (IMEX) Runge-Kutta methods play a major rule in the numerical treatment of differential systems governed by stiff and non-stiff terms. This paper discusses order conditions and symplecticity properties of a class of IMEX Runge–Kutta methods in the context of optimal control problems. The analysis of the schemes is based on the continuous optimality system. Using suitable trans...

Particle systems have been widely employed to animate deformable objects. In order to achieve real time capable systems often simplifications have been made to reduce the computational costs for solving the ODE at the expense of numerical and physical correctness. Implicit-Explicit (IMEX) methods provide a way to solve partly stiff systems efficiently, if the system meets some requirements. The...

In this paper, the unsteady Navier-Stokes Takagi-Sugeno (T-S) fuzzy equations (UNSTSFEs) are represented as a differential algebraic system of strangeness index one by applying any spatial discretization. Since such differential algebraic systems have a difficulty to solve in their original form, most approaches use some kind of index reduction. While processing this index reduction, it is impo...

In order to embark on the development of numerical schemes for stiff problems, we have studied a model of relaxing heat flow. To isolate those errors unavoidably associated with discretization, a method of characteristics is developed, containing three free parameters depending on the stiffness ratio. It is shown that such “decoupled” schemes do not take into account the interaction between the...

In this paper, a novel hybrid method based on learning algorithmof fuzzy neural network and Newton-Cotesmethods with positive coefficient for the solution of linear Fredholm integro-differential equation of the second kindwith fuzzy initial value is presented. Here neural network isconsidered as a part of large field called neural computing orsoft computing. We propose alearning algorithm from ...

We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh's extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation techni...

The Liu process is a fuzzy whose membership function symmetric on an expected value. object of this paper was differential equation driven by process. Since the existing Euler solving methods (explicit scheme, semi-implicit and implicit scheme) have same convergence, to compare them, we presented four stabilities, i.e., asymptotical stability, mean square exponential A stability. By choosing sp...

We introduce a solver for stiff ordinary differential equations (ODEs) that is based on the deferred correction scheme for the corresponding Picard integral equation. Our solver relies on the assumption that the solution can be accurately represented by a combination of carefully selected complex exponentials. The solver’s accuracy and stability rely on the computation of highly accurate quadra...