The new class of multistep multiderivative hybrid methods for the numerical solution of chemical stiff systems of first order IVPs

Khalsaraei, Mohammad Mehdizadeh; Shokri, Ali; Molayi, Maryam

doi:10.1007/s10910-020-01160-z

Cited by 7 publications

(12 citation statements)

References 81 publications

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“…The results generated by the developed 3POBBDF(5) method are displayed in Tables 3, 4, 5, 6. In Table 3, comparison on the basis of absolute error was made using the 3POBBDF(5) of order 5 at the point x = 2 with the methods of Khalsaraei and Molayi [48] and Ismail's method [49] at the stepsizeh = 10 −5 . In Table 4, 3POBBDF (5) method is integrated at h = 10 −5 and the direct comparison has been made with the two step hybrid method with one off-step point [48] by taking the solution points atx = 180 .…”

Section: Discussionmentioning

confidence: 99%

“…In Table 3, comparison on the basis of absolute error was made using the 3POBBDF(5) of order 5 at the point x = 2 with the methods of Khalsaraei and Molayi [48] and Ismail's method [49] at the stepsizeh = 10 −5 . In Table 4, 3POBBDF (5) method is integrated at h = 10 −5 and the direct comparison has been made with the two step hybrid method with one off-step point [48] by taking the solution points atx = 180 . Table 3 shows that the 3POBBDF( 5) is more accurate and performs relatively better than the method [48] and significantly better than the method [49].…”

Section: Discussionmentioning

confidence: 99%

“…Error in [48] Error in [49] 2.0 y 1 0.00003616933169289 two-step hybrid method by Khalsaraei and Molayi [48], and Ismail's method [49], the 3POBBDF( 5) method provides more accurate results in terms of Absolute error.…”

Section: Problem 51 (Stiff Chemical Reaction Problem)mentioning

confidence: 99%

“…with the initial conditions as y 1 (0) = 1 and y 2 (0) = 1 having exact solutions as, This problem is solved at x = 50 by the new method and compared the results with forth order Two step hybrid method with one off-step point [48]. Here the stepsize h = 0.05 is used for compared and proposed methods.…”

Section: Problem 54 (Stiff Chemical Reaction Problem)mentioning

confidence: 99%

“…Several points have been examined for the selection of off-step points and hence it was concluded that selecting the points where the step is halved will lead to zero-stable formulae. Compared to the methods developed by Khalsaraei and Molayi [48], and Ismail [49], the advantage of the proposed method is that the solutions are approximated with off-step points concurrently and provide better accuracy. The organization of the paper is as follow; Section 2 briefly describes the formulation of the method.…”

Section: Introductionmentioning

confidence: 99%

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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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