Forward Difference Formula for the First Derivative
نویسنده
چکیده
Study the interplay between roundoff error and truncation error in using the forward difference formula for the first derivative. Directory • Table of
منابع مشابه
A distinct numerical approach for the solution of some kind of initial value problem involving nonlinear q-fractional differential equations
The fractional calculus deals with the generalization of integration and differentiation of integer order to those ones of any order. The q-fractional differential equation usually describe the physical process imposed on the time scale set Tq. In this paper, we first propose a difference formula for discretizing the fractional q-derivative of Caputo type with order and scale index . We es...
متن کاملNumerical solution for boundary value problem of fractional order with approximate Integral and derivative
Approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. In this paper with central difference approximation and Newton Cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. Three...
متن کاملAn Explicit Numerical Method for the Fractional Cable Equation
An explicit numerical method to solve a fractional cable equation which involves two temporal Riemann-Liouville derivatives is studied. The numerical difference scheme is obtained by approximating the first-order derivative by a forward difference formula, the Riemann-Liouville derivatives by the Grünwald-Letnikov formula, and the spatial derivative by a three-point centered formula. The accura...
متن کاملMatrix Exponentiation and the Frank-Kamenetskii Equation
Long time solutions to the Frank-Kamenetskii partial differential equation modelling a thermal explosion in a vessel are obtained using matrix exponentiation. Spatial derivatives are approximated by high-order finite difference approximations. A forward difference approximation to the time derivative leads to a Lawson-Euler scheme. Computations performed with a BDF approximation to the time der...
متن کاملON A FORMULA FOR THE nTH DERIVATIVE AND ITS APPLICATIONS
In this paper we obtain a formula which involves the n th derivative of the first order divided difference and a corresponding inequality for functions whose (n + 1)-th derivative belongs to a L p space. These results are a generalization of the results from [1] and [2]. Finally, some examples are given.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004