In this paper, we study the numerical solution of hybrid fuzzy differential equations by using differential transformation method (DTM). This is powerful method which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution. Several numerical examples are given and by comparing the numerical results obtained from DTM  and  predi...

Received 17 September 2011; revised 10 November 2011; accepted 17 November 2011. ———————————————————————————————Abstract In this paper, the fuzzy solution of non-linear fuzzy Volterra integro-differential equation (NFIDE) is approximated. To do this, we define a sequence of fuzzy functions which approximate the fuzzy solution of this type of equations and finally, we estimate upper bound of the...

There are many laws stating the behavior of the physical world involves quantities which are changing with respect to another quantities and the mathematical expressions of such laws are differential equations. There are numbers of problems of various fields like science, engineering-technology, social science etc. involves differential equations. The researchers have developed many analytical ...

This paper focuses on the fuzzy Volterra integro-differential equation of nth order of the second-kind with nonlinear fuzzy kernel and initial values. The derived integral equations are solvable, the solutions of which are unique under certain conditions. The existence and uniqueness of the solutions are investigated in a theorem and an upper boundary is found for solutions. Comparison of the e...

In this paper, we introduce a fictitious dynamics for describing the only fast relaxation of a stiff ordinary differential equation (ODE) system towards a stable low-dimensional invariant manifold in the phase-space (slow invariant manifold SIM). As a result, the demanding problem of constructing SIM of any dimensions is recast into the remarkably simpler task of solving a properly devised ODE ...

In this study, differential transform method (DTM) is applied to fuzzy integro-differential equation. The concept of generalized Hdifferentiability is used. If the equation has a solution in terms of the series expansion of known functions; this powerful method catches the exact solution. Some numerical examples are also given to illustrate the superiority of the method. All rights reserved.

Variable-step (VS) second derivative $k$-step $3$-stage Hermite--Birkhoff--Obrechkoff (HBO) methods of order $p=(k+3)$, denoted by HBO$(p)$ are constructed as a combination of linear $k$-step methods of order $(p-2)$ and a second derivative two-step diagonally implicit $3$-stage Hermite--Birkhoff method of order 5 (DIHB5) for solving stiff ordinary differential equations. The main reason for co...

In this paper, we introduce a fictitious dynamics for describing the only fast relaxation of a stiff ordinary differential equation (ODE) system towards a stable low-dimensional invariant manifold in the phase-space (slow invariant manifold SIM). As a result, the demanding problem of constructing SIM of any dimensions is recast into the remarkably simpler task of solving a properly devised ODE ...

A partitioned implicit-explicit orthogonal Runge-Kutta method (PIROCK) is proposed for the time integration of diffusion-advection-reaction problems with possibly severely stiff reaction terms and stiff stochastic terms. The diffusion terms are solved by the explicit second order orthogonal Chebyshev method (ROCK2), while the stiff reaction terms (solved implicitly) and the advection and noise ...