Splitting methods are frequently used in solving stiff differential equations, it is common to split the system of equations into a stiff and a nonstiff part. The classical theory for the local order of consistency is valid only for stepsizes which are smaller than what one would typically prefer to use in the integration. Error control and stepsize selection devices based on classical local or...

In the previous note it was shown how L-Systems can be used to numerically solve systems of partial differential equations, for a constant or growing medium, and the method was applied to computer graphics purposes. The LSystem from the previous section employed a forward Euler method for finite differencing. Although simple to implement, the forward Euler method is in many case inadequate, for...

A new variant of Local Linearization (LL) method is proposed for the numerical (strong) solution of differential equations driven by (additive) alpha-stable Lévy motions. This is studied through simulations making emphasis in comparison with the Euler method from the viewpoint of numerical stability. In particular, a number of examples of stiff equations are shown in which the Euler method has ...

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 ...

Many methods have been proposed for numerically integrating the differential-algebraic systems arising from the Euler-Lagrange equations for constrained motion. These are based on various problem formulations and discretizations. We offer a critical evaluation of these methods from the standpoint of stability. Considering a linear model, we first give conditions under which the differential-alg...

in this article differential transformation method (dtms) has been used to solve neutral functional-differential equations with proportional delays. the method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series solution with fast convergence rate. exact solutions can also be obtained from the kno...

in this paper, we apply the differential transform (dt) method for finding approximate solution of the system of linear and nonlinear volterra integro-differential equations with variable coefficients, especially of higher order. we also obtain an error bound for the approximate solution. since, in this method the coefficients of taylor series expansion of solution is obtained by a recurrence r...