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 ...

The commonly used one step methods and linear multi-step methods all have a global error that is of the same order as the local truncation error. In fact, this is true of the entire class of general linear methods. In practice, this means that the order of the method is typically defined solely by order conditions which are derived by studying the local truncation error. In this work we investi...

Local grid refinement aims to optimise the relationship between accuracy of the results and number of grid nodes. In the context of the finite volume method no single local refinement criterion has been globally established as optimum for the selection of the control volumes to subdivide, since it is not easy to associate the discretisation error with an easily computable quantity in each contr...

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 ...

We consider approximate solutions to nonlinear hyperbolic conservation laws. If the exact solution is unavailable, the truncation error may be the only quantitative measure for the quality of the approximation. We propose a new way of estimating the local truncation error, through the use of localized test-functions. In the convex scalar case, they can be converted into L∞loc estimates, followi...

A posteriori estimation of the numerical error sensitivity to the local truncation error is addressed using adjoint model endowed with the information on the error field. The numerical error is estimated from the solution of the linear tangent model (LTM) or from a Richardson extrapolation. The local truncation error used in the LTM is obtained by the action of a high order finite-difference st...

Predictor-corrector (PC) methods for the numerical solution of stiff ODEs can be extended to include the second derivative of the solution. In this paper, we consider second derivative PC methods with the three-step second derivative Adams-Bashforth as predictor and two-step second derivative Adams-Moulton as corrector which both methods have order six. Implementation of the proposed PC method ...

Balanced model truncation has been considered by many authors, since it is a simple and, nevertheless, efficient model reduction technique. In many cases the approximation error may be bounded by a function of the neglected singular values. In this paper the performance of balanced truncation of state space models for ARMA processes is analysed, where the goodness of fit is measured by the asym...