in this paper, we consider first-order fuzzy differential equations with initial value conditions. the convergence, consistency and stability of difference method for approximating the solution of fuzzy differential equations involving generalized h-differentiability, are studied. then the local truncation error is defined and sufficient conditions for convergence, consistency and stability of ...

a simple new closed form of the green function for axisymmetric magnetostatic problemsis found analytically in cylindrical coordinates. the result is verified by applying several examples.

Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...

in this paper we propose a method for solving some well-known classes of lane-emden type equations which are nonlinear ordinary differential equations on the semi-in nite domain. the proposed approach is based on an unsupervised combined arti cial neural networks (ucann) method. firstly, the trial solutions of the differential equations are written in the form of feed-forward neural networks co...

We present for the first time an analytical approach for determining the time of firing of multicomponent nonlinear stochastic neuronal models. We apply the theory of first exit times for Markov processes to the Fitzhugh-Nagumo system with a constant mean gaussian white noise input, representing stochastic excitation and inhibition. Partial differential equations are obtained for the moments of...

in this article, we study the analytical solutions of different parabolic heat equations with different boundaryconditions in the form of multi-term fractional differential equations. then we compare these analytical solutions with numerical finite difference methods. this comparison demonstrates the accuracy of the analytical and numerical methods presented here.

the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...

in this paper, we consider an implicit block backwarddifferentiation formula (bbdf) for solving volterraintegro-differential equations (vides). the approach given in thispaper leads to numerical methods for solving vides which avoid theneed for special starting procedures. convergence order and linearstability properties of the methods are analyzed. also, methods withextensive stability region ...

the numerical methods are of great importance for approximating the solutions of nonlinear ordinary or partial differential equations, especially when the nonlinear differential equation under consideration faces difficulties in obtaining its exact solution. in this latter case, we usually resort to one of the efficient numerical methods. in this paper, the chebyshev collocation method is sugge...