Global error estimation and the backward differentiation formulas
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Global error estimation and the backward differentiation formulas

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Published by Dept. of Computer Science, University of Illinois at Urbana-Champaign in Urbana, IL (1304 W. Springfield Ave., Urbana 61801) .
Written in English

Subjects:

  • Differential equations -- Numerical solutions -- Data processing.,
  • Error analysis (Mathematics)

Book details:

Edition Notes

Other titlesBackward differentiation formulas.
Statementby Robert D. Skeel.
SeriesReport / Department of Computer Science, University of Illinois at Urbana-Champaign ;, no. UIUCDCS-R-86-1291, Report (University of Illinois at Urbana-Champaign. Dept. of Computer Science) ;, no. UIUCDCS-R-86-1291.
Classifications
LC ClassificationsQA76 .I4 no. 1291, QA371 .I4 no. 1291
The Physical Object
Pagination20 p. ;
Number of Pages20
ID Numbers
Open LibraryOL2496124M
LC Control Number87620742

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Numerical Differentiation Differentiation is a basic mathematical operation with a wide range of applica-tions in many areas of science. It is therefore important to have good meth-ods to compute and manipulate derivatives. You probably learnt the basic rules of differentiation in school — symbolic methods suitable for pencil-and-paper. The formulas are called decoupled backward differentiation formulas, and they are derived from the classical formulas by restricting the implicit part to the diagnonal sub-system. @article{osti_, title = {Variable order and variable step-size integration method for transient analysis programs}, author = {Kato, T and Ikeuchi, K}, abstractNote = {A variable order and variable step-size integration method using the backward differentiation formulas (VOVS-BDF) is introduced to optimize numerical integration orders and step-sizes for power transient analysis. The Euler method is + = + (,). so first we must compute (,).In this simple differential equation, the function is defined by (,).We have (,) = (,) =By doing the above step, we have found the slope of the line that is tangent to the solution curve at the point (,).Recall that the slope is defined as the change in divided by the change in, or /.. The next step is to multiply the above value.

The book also reviews the existing stiff codes based on the implicit/semi-implicit, singly/diagonally implicit Runge-Kutta schemes, the backward differentiation formulas, the second derivative formulas, as well as the related extrapolation processes. Chapter 7: Numerical Differentiation 7–16 Numerical Differentiation The derivative of a function is defined as if the limit exists • Physical examples of the derivative in action are: – Given is the position in meters of an object at time t, the first derivative with respect to t,, is the velocity in. It is possible to write more accurate formulas than () for the first derivative. For example, a more accurate approximation for the first derivative that is based on theFile Size: KB.   Techniques for maintaining the numerical consistency of equality and inequality invariants known to be obeyed by the true solutions of ODES are discussed. Shampine [11] has examined the problem and made some recommendations for one-step methods. A general framework is used to justify ular form of his technique for both one-step and multistep methods in the case of equality Cited by:

A new theory is presented, in which a generalized kinematic similarity transformation is used to diagonalize linear differential systems. No matrices of Jordan form are needed. The relation to Lyapunov’s classical stability theory is explored, and asymptotic estimates of fundamental solutions are given. Finally, some possible numerical applications of the presented theory are by:   Dahlquist, G., Liniger, W. and Nevanlinna, O.: Stability of Two-Step Methods for Variable Integration Steps. IBM Research Report RC , September ; submitted to Cited by: 7. Euler’s Method, Taylor Series Method, Runge Kutta Methods, Multi-Step Methods and Stability. REVIEW: We start with the differential equation dy(t) dt = f (t,y(t)) () y(0) = y0 This equation can be nonlinear, or even a system of nonlinear equations (in which case y is .   To view the rest of this content please follow the download PDF link above.