Two-Step Hybrid Block Method for Solving First Order Ordinary Differential Equations Using Power Series Approach

Ajileye, G; Amoo, S; Ogwumu, O. D.

doi:10.9734/jamcs/2018/41557

Cited by 4 publications

(6 citation statements)

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“…In Tab. 1, it is observed that the proposed method reduces the error, approximately by the average of 33% and 41% compared to [30,43] respectively. The efficiency of the proposed method can also be checked from Tabs.…”

Section: Resultsmentioning

confidence: 85%

“…Tab. 1 depicts the comparison of the numerical outcomes by 3-point hybrid block AMM with the two-step block hybrid method by Ajileye et al [30] and 3-step hybrid Adams type methods by Yahaya et al [43] for the SIR model. Absolute error was computed by finding the difference between the exact solution and proposed method's solution at distinctive values of t. The solution of the 3-point hybrid block AMM performs better than [30,43].…”

Section: Resultsmentioning

confidence: 99%

“…The main persistence of [9] is to generate a higher-order block algorithm with excellent stability properties, such as A-stability, for addressing various types of IVPs. Reference [30] worked on the hybrid block approach with power series expansion which would aid in the development of a more computationally stable integrator capable of solving problems relating to first-order differential equations of the form Eq. (1).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimized Hybrid Block Adams Method for Solving First Order Ordinary Differential Equations

Soomro¹,

Zainuddin²,

Daud³

et al. 2022

Computers, Materials &Amp; Continua

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Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost. The block methods were developed with the intent of obtaining numerical results on numerous points at a time and improving computational efficiency. Hybrid block methods for instance are specifically used in numerical integration of initial value problems. In this paper, an optimized hybrid block Adams block method is designed for the solutions of linear and nonlinear first-order initial value problems in ordinary differential equations (ODEs). In deriving the method, the Lagrange interpolation polynomial was employed based on some data points to replace the differential equation function and it was integrated over a specified interval. Furthermore, the convergence properties along with the region of stability of the method were examined. It was concluded that the newly derived method is convergent, consistent, and zero-stable. The method was also found to be A-stable implying that it covers the whole of the left/negative half plane. From the numerical computations of absolute errors carried out using the newly derived method, it was found that the method performed better than the ones with which we compared our results with. The method also showed its superiority over the existing methods in terms of stability and convergence.

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Section: Resultsmentioning

confidence: 85%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimized Hybrid Block Adams Method for Solving First Order Ordinary Differential Equations

Soomro¹,

Zainuddin²,

Daud³

et al. 2022

Computers, Materials &Amp; Continua

View full text Add to dashboard Cite

show abstract

“…• IGRKM represents the implicit Gauss-Legendre method of the sixth order in [4]. • THBM is the two-step hybrid block method in [20]. • FE denotes the total number of function evaluations.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…Some of these approximation techniques comprise embedded Runge-Kutta type methods, general linear methods, Numerov-type methods, spline methods, finite difference, Nyström methods, space-time numerical methods, block methods, and various collocation methods. These methods are extensively discussed in various research papers and books, such as [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

A New Hybrid Block Method for Solving First-Order Differential System Models in Applied Sciences and Engineering

Rufai,

Carpentieri,

Ramos

2023

Fractal Fract

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This paper presents a new hybrid block method formulated in variable stepsize mode to solve some first-order initial value problems of ODEs and time-dependent partial differential equations in applied sciences and engineering. The proposed method is implemented considering an adaptive stepsize strategy to maintain the estimated error in each step within a specified tolerance. In order to evaluate the performance and usefulness of the proposed technique in real-world applications, several differential problems from applied sciences and engineering, such as the SIR model, Jacobi elliptic function problem, and chemical reactions problems, are solved numerically. The results of numerical simulations in this work demonstrate that the proposed method is more efficient than other existing numerical methods used for comparisons.

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Implicit Four-Point Hybrid Block Integrator for the Simulations of Stiff Models

Sunday

Kumleng

Kamoh

et al. 2022

J. Nig. Soc. Phys. Sci.

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Over the years, the systematic search for stiff model solvers that are near-optimal has attracted the attention of many researchers. An attempt has been made in this research to formulate an implicit Four-Point Hybrid Block Integrator (FPHBI) for the simulations of some renowned rigid stiff models. The integrator is formulated by using the Lagrange polynomial as basis function. The properties of the integrator which include order, consistency, and convergence were analyzed. Further analysis showed that the proposed integrator has an A-stability region. The A-stability nature of the integrator makes it more robust and fitted for the simulation of stiff models. To test the computational reliability of the new integrator, few well-known technical stiff models such as the pharmacokinetics, Robertson and Van der Pol models were solved. The results generated were then compared with those of some existing methods including the MATLAB solid solvent, ode 15s. From the results generated, the new implicit FPHBI performed better than the ones with which we compared our results with.

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Two-Step Hybrid Block Method for Solving First Order Ordinary Differential Equations Using Power Series Approach

Cited by 4 publications

References 0 publications

Optimized Hybrid Block Adams Method for Solving First Order Ordinary Differential Equations

Optimized Hybrid Block Adams Method for Solving First Order Ordinary Differential Equations

A New Hybrid Block Method for Solving First-Order Differential System Models in Applied Sciences and Engineering

Implicit Four-Point Hybrid Block Integrator for the Simulations of Stiff Models

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