A one-step 4-stage Hermite-Birkhoff-Taylor method of order 12, denoted by HBT(12)4, is constructed for solving nonstiff systems of first-order differential equations of the form y′ = f(x, y), y(x0) = y0. The method uses derivatives y′ to y(9) as in Taylor methods combined with a 4-stage Runge-Kutta method. Forcing an expansion of the numerical solution to agree with a Taylor expansion of the tr...

In this survey talk we aim to clarify the close relationships between the operators of the generalized fractional calculus (GFC), some classes of generalized hypergeo-metric functions and generalizations of the classical integral transforms. The GFC developed in [1] is based on the essential use of the Special Functions (SF). The generalized (multiple) fractional integrals and derivatives are d...

Fuzzy differential equation models are suitable where uncertainty exists for real-world phenomena. Numerical techniques used to provide an approximate solution these in the absence of exact solution. However, existing studies that have developed numerical solving FIVPs possess absolute error accuracy could be improved. This is as a result low order and non-self-starting properties by previous s...

many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. for the efficient solution of the above mentioned problems, linear multistep methods or runge-kutta technique are used. for the simulation of chemical procedures the ra...

Many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. For the efficient solution of the above mentioned problems, linear multistep methods or Runge-Kutta technique are used. For the simulation of chemical procedures the ra...