Optimization of one step block method with three hybrid points for solving first-order ordinary differential equations

Kashkari, Bothayna S.; Syam, Muhammed I.

doi:10.1016/j.rinp.2018.12.015

Cited by 16 publications

(10 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The effect of learning methods and motivation on learning outcomes of long jump skills 428 command teaching styles, this means that the first hypothesis has different teaching styles on the long jump skills learning outcomes that have been tested (Ida Zubaida et al, 2021). The block method is a grouping of effective study hours in units of time that is summarized to students to follow and receive learning materials optimally and intact (Kashkari & Syam, 2019). The block exercise is a training schedule in which one skill variation is repeated practice before the exercise effort is given to another variation (Coker, 2017).…”

Section: Syahruddinmentioning

confidence: 99%

The effect of learning methods and motivation on learning outcomes of long jump skills

Syahruddin

2022

SPORTIF

View full text Add to dashboard Cite

The results of learning physical education skills were not limited to physical development but also mental development and motivation to learn. The purpose of this study was to determine the effect of the block method (BM) and the play-based random method (RM) on long jump skills (JLS) in terms of motivation (MTV). This type of research is quasi-experimental with a 2x2 factorial design. A sample of 20 Samiun Makassar public primary school students was randomly selected and divided into four groups. Treatment research for eight weeks. Before treatment, the sample was divided into two, high motivation (MTVH) and low motivation (MTVL), through questionnaires and the final test of long jump skills learning outcomes (JLS). The results showed that BM significantly increased JLS compared to RM (P<0.05). There was a significant interaction between Mt and MTV (P<0.05). The MTVH student group using MBB1 had better JLS than MRB1 (P<0.05). The group of students who had MTVL had no difference in results between MBB2 and MRB2 (P>0.05). KLJ in physical education for elementary school students is very good at using MB, and the teacher increases MTV during learning.

show abstract

Section: Syahruddinmentioning

confidence: 99%

The effect of learning methods and motivation on learning outcomes of long jump skills

Syahruddin

2022

SPORTIF

View full text Add to dashboard Cite

show abstract

“…Nevertheless, the most effective formulation was achieved by simply reformulating the approach in a manner that reduces the frequency of occurrences of the source term f. A comparison between the proposed economic reformulation and existing methods from the literature revealed that the former exhibited superior performance. In their study, [19] introduced an optimized one-step hybrid block technique designed specifically for the optimization of first-order initial value problems (IVPs). The approach involved the selection of three hybrid points in a judicious manner to maximize the LTEs of the primary equations for the block.…”

Section: Introductionmentioning

confidence: 99%

One-step three-parameter optimized hybrid block method for solving first order initial value problems of ordinary differential equations

E. A. Areo,

Gbenro,

Olabode

et al. 2024

J. Math. Anal. Model.

View full text Add to dashboard Cite

A one-step three-parameter optimized hybrid block method and second derivative hybrid block method with optimized points were proposed to solve first-order ordinary differential equations. The techniques of interpolation and collocation were adopted for the derivation of the methods using a three-parameter approximation. The hybrid points were obtained by optimizing the local truncation error of the method. The schemes obtained were reformulated to reduce the number of occurrences of the source term. The hybrid points were used in the derivation of the second derivative hybrid block method. The discrete schemeswere produced as a by-product of the continuous scheme and used to simultaneously solve initial value problems (IVPs) in block mode. The resulting schemes are self-starting, do not require the creation of individual predictors, and are consistent, zero-stable, and convergent. The accuracy and efficiency of the methods were ascertained using several numerical test problems. The numerical results were favourably compared to some techniques from the cited literature.

show abstract

“…Despite having many advantages, the block method also possessed a major setback which pointed out that the order of interpolation points must not exceed the order of the differential equations [36,37]. Because of this setback, addition of offstep points in the block were introduced and named as hybrid method.…”

Section: Introductionmentioning

confidence: 99%

“…Because of this setback, addition of offstep points in the block were introduced and named as hybrid method. Hybrid methods are highly efficient and have been reported to circumvent the "Dahlquist Zero-Stability Barrier" condition by introducing function evaluation at off-step points which takes some time in its development but provides better approximation than two conventional methods (Runge-Kutta and linear multistep methods) [13,36]. [38] proposed function evaluation at an off-step and named as "Hybrid" method.…”

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

View full text Add to dashboard Cite

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.

show abstract

Optimization of one step block method with three hybrid points for solving first-order ordinary differential equations

Cited by 16 publications

References 6 publications

The effect of learning methods and motivation on learning outcomes of long jump skills

The effect of learning methods and motivation on learning outcomes of long jump skills

One-step three-parameter optimized hybrid block method for solving first order initial value problems of ordinary differential equations

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

Contact Info

Product

Resources

About