منابع مشابه
On Taylor Model Based Integration of ODEs
The numerical solution of initial value problems (IVPs) for ODEs is one of the fundamental problems in computation. Today, there are many well-established algorithms for solving IVPs. However, traditional integration methods usually provide only approximate values for the solution. Precise error bounds are rarely available. The error estimates, which are sometimes delivered, are not guaranteed ...
متن کاملImproved Taylor Expansion method in Ising model
We apply improved Taylor expansion method which is one of the variational schemes to Ising model in two-dimensions. It enables us to evaluate free energy and magnetization at strong coupling regions from weak coupling expansion even in the presence of the phase transition. We determine approximated transition point in this scheme. In the presence of external magnetic field we can see not only s...
متن کاملPerformance of Taylor Model Methods for Validated Integration of ODEs
The performance of various Taylor model (TM)-based methods for the validated integration of ODEs is studied for some representative computational problems. For nonlinear problems, the advantage of the method lies in the ability to retain dependencies of final conditions on initial conditions to high order, leading to the ability to treat large boxes of initial conditions for extended periods of...
متن کاملImproved Taylor Expansion method in the Ising model
We apply an improved Taylor expansion method, which is a variational scheme to the Ising model in two dimensions. This method enables us to evaluate the free energy and magnetization in strong coupling regions from the weak coupling expansion, even in the case of a phase transition. We determine the approximate value of the transition point using this scheme. In the presence of an external magn...
متن کاملApproximation, Numerical Differentiation and Integration Based on Taylor Polynomial
We represent new estimates of errors of quadrature formula, formula of numerical differentiation and approximation using Taylor polynomial. To measure the errors we apply representation of the remainder in Taylor formula by least concave majorant of the modulus of continuity of the n−th derivative of an n−times differentiable function. Our quantitative estimates are special applications of a mo...
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ژورنال
عنوان ژورنال: Baghdad Science Journal
سال: 2009
ISSN: 2411-7986,2078-8665
DOI: 10.21123/bsj.6.1.222-230