Block method for third order ordinary differential equations

Zainuddin, Nooraini; İbrahim, Zarina Bibi

doi:10.1063/1.4995919

Cited by 3 publications

(1 citation statement)

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“…Gear [21] initially introduced the BDF, which is known to be efficient in handling complex stiff ODE problems. This BDF approach has been extended in papers such as [15,[22][23][24][25]. Single-step and multi-step block techniques are the two types of block methods.…”

Section: Introductionmentioning

confidence: 99%

3-Point block backward differentiation formula with an off-step point for the solutions of stiff chemical reaction problems

et al. 2022

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A major challenge in simulating chemical reaction processes is integrating the stiff systems of Ordinary Differential Equations (ODEs) describing the chemical reactions due to stiffness. Thus, it would be of interest to search systematically for stiff solvers that are close to optimal for such problems. This paper presents an implicit 3-Point Block Backward Differentiation Formula with one off-step point (3POBBDF) for the solutions of first-order stiff chemical reaction problems. In deriving the method, the Lagrange polynomial was adopted as the basis function. The paper further analyses the basic properties of the 3POBBDF which include order of accuracy, consistence, zero-stability, and convergence. The stability region as well as the interval of instability of the method was also computed. To demonstrate the accuracy of the proposed approach, some famous stiff chemical reaction problems such as Robertson problem and Chemical AKZO were solved, and the results obtained were compared with those of some existing methods. The results obtained clearly show that the 3POBBDF performs better than the existing methods with which we compared our results.

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Section: Introductionmentioning

confidence: 99%