TITLE

# Direct Block Backward Differentiation Formulas for Solving Second Order Ordinary Differential Equations

AUTHOR(S)
Ibrahim, Zarina Bibi; Suleiman, Mohamed; Othman, Khairil Iskandar
PUB. DATE
June 2008
SOURCE
Proceedings of World Academy of Science: Engineering & Technolog;Jun2008, Vol. 42, p57
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
In this paper, a direct method based on variable step size Block Backward Differentiation Formula which is referred as BBDF2 for solving second order Ordinary Differential Equations (ODEs) is developed. The advantages of the BBDF2 method over the corresponding sequential variable step variable order Backward Differentiation Formula (BDFVS) when used to solve the same problem as a first order system are pointed out. Numerical results are given to validate the method.
ACCESSION #
33132469

## Related Articles

• Partitioning Ordinary Differential Equations Using Multistep Formulas. Suleiman, Mohamed; Ibrahim, Zarina Bibi; Othman, Khairil Iskandar // Proceedings of World Academy of Science: Engineering & Technolog;Jun2008, Vol. 42, p52

This paper focuses on solving Ordinary Differential Equations (ODEs) using partitioning technique known as Intervalwise Partitioning Block (IPB) method which is based on Block Backward Differentiation Formulas (BBDF) and Block Adams Formulas. Method based on BBDF requires Newton-like iteration...

• Parallel Block Backward Differentiation Formulas for Solving Ordinary Differential Equations. Othman, Khairil Iskandar; Ibrahim, Zarina Bibi; Suleiman, Mohamed // Proceedings of World Academy of Science: Engineering & Technolog;Jun2008, Vol. 42, p54

A parallel block method based on Backward Differentiation Formulas (BDF) is developed for the parallel solution of stiff Ordinary Differential Equations (ODEs). Most common methods for solving stiff systems of ODEs are based on implicit formulae and solved using Newton iteration which requires...

• Unstable extremal surfaces of the ï¿½Shiffman functionalï¿½ spanning rectifiable boundary curves. Jakob, Ruben // Calculus of Variations & Partial Differential Equations;Mar2007, Vol. 28 Issue 3, p383

In this paper we derive a sufficient condition for the existence of extremal surfaces of a parametric functional $$\mathcal{J}$$ with a dominant area term, which do not furnish global minima of $$\mathcal{J}$$ within the class $$\mathcal{C}^*(\Gamma )$$ of H 1,2-surfaces spanning an arbitrary...

• Analytic Solutions of Some Self-Adjoint Equations by Using Variable Change Method and Its Applications. Delkhosh, Mehdi; Delkhosh, Mohammad // Journal of Applied Mathematics;2012, p1

Many applications of various self-adjoint differential equations, whose solutions are complex, are produced (Arfken, 1985; Gandarias, 2011; and Delkhosh, 2011). In this work we propose a method for the solving some self-adjoint equations with variable change in problem, and then we obtain a...

• The High Contact Principle with Reward Functions Involving Initial Points. Dongmei Guo; Yi Hu; Jiankang Zhang; Chunli Chu // Mathematical Problems in Engineering;2014, p1

This paper examines a class of general optimal stopping problems in which reward functions depend on initial points. Two points of view on the initial point are introduced: one is to view it as a constant, and the other is to view it as a constant process starting from the point. Based on the...

• A new upper bound for ( n, 3)-MAX-SAT. Bliznets, I. // Journal of Mathematical Sciences;Jan2013, Vol. 188 Issue 1, p1

It is still not known whether the satisfiability problem (SAT), and hence the maximum satisdiability problem (MAX-SAT), can be solved in time poly(| F|) c for c < 2, where c is a constant, n is the number of variables, and F is the input formula. However, such bounds are known for some special...

• L p-PoincarÃ© inequality for general symmetric forms. Yong Hua Mao // Acta Mathematica Sinica;Dec2009, Vol. 25 Issue 12, p2055

L p PoincarÃ© inequalities for general symmetric forms are established by new Cheegerâ€™s isoperimetric constants. L p super-PoincarÃ© inequalities are introduced to describe the equivalent conditions for the L p compact embedding, and the criteria via the new Cheegerâ€™s constants...

• Efficient Technique for Solving Stiff Delay Differential Equations in Variable Stepsize Variable Order. Isa, Nora Baizura Mohd; Ishak, Fuziyah; Othman, Khairil Iskandar // AIP Conference Proceedings;2014, Vol. 1605, p52

In this paper, we describe the development of predictor corrector variable stepsize variable order method based on backward differentiation formula. The formula is represented in divided difference form where the coefficients of differentiation are computed by a simple recurrence relation. This...

• On Some New Impulsive Integral Inequalities. Jianli Li // Journal of Inequalities & Applications;2008, Vol. 2008, p1

The article discusses a study which establish new impulsive integral inequalities connected to certain integral inequalities coming from the theory of differential equalities. The study aims to create new impulsive integral inequalities like the Bihari's inequalities. It states that differential...

Share