A Finite Difference Method of High Order Accuracy for the Solution of Two-Point Boundary Value Problems

Pandey, Pramod Kumar

doi:10.14513/actatechjaur.v7.n2.242

Cited by 5 publications

(6 citation statements)

References 16 publications

(18 reference statements)

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“…An implementation of fixed step size is the most commonly used in deriving numerical method (Anakira et al 2013;Jator 2012;Jikantoro et al 2015;Pandey 2014). However, the utilization of variable step size strategy in the numerical method had been adopted by several researchers such as Cash and Girdlestone (2006), Majid and Suleiman (2006), Majid et al (2012) and Waeleh et al (2011b).…”

Section: (1)mentioning

confidence: 99%

Numerical Algorithm of Block Method for General Second Order ODEs using Variable Step Size

Waeleh¹,

Majid²

2017

JSM

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This paper outlines an alternative algorithm for solving general second order ordinary differential equations (ODEs). Normally, the numerical method was designed for solving higher order ODEs by converting it into an n-dimensional first order equations with implementation of constant step length. Nevertheless, this involved a lot of computational complexity which led to consumption a lot of time. Consequently, a direct block multistep method with utilization of variable step size strategy is proposed. This method was developed for computing the solution at four points simultaneously and the derivation based on numerical integration as well as using interpolation approach. The convergence of the proposed method is justified under suitable conditions of stability and consistency. Five numerical examples are considered and some comparisons are made with the existing methods for demonstrating the validity and reliability of the proposed algorithm.

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Section: (1)mentioning

confidence: 99%

Numerical Algorithm of Block Method for General Second Order ODEs using Variable Step Size

Waeleh¹,

Majid²

2017

JSM

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“…In the future, we plan to modify our method in the following three aspects: (1) Apply our method to noncoordinate system; (2) Find out more solutions to the scattering and optimization. (3) Conduct more in-depth research on mathematical analysis of our method, [21][22][23][24][25][26][27][28][29] is our potential research basis.…”

Section: Conclusion and Summarymentioning

confidence: 99%

Combination of Cloud Computing and Internet of Things (IOT) in Medical Monitoring Systems

Liu¹,

Dong²,

Guo³

et al. 2015

IJHIT

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With the fast development of cloud computing and computer science technology, the combination of the IOT and clod computing in the medical-assisted environment is urgently needed. The prior research focus more on individual development of the single technique, quite a less research on the field of medical monitoring and managing service application have been conducted. Therefore, in this paper, we study and analyze the application of cloud computing and the Internet of Things on the field of medical environment. We are trying to make the combination of the two kinds of technology monitoring and management information system in hospital. Remote monitoring cloud platform architecture model (RMCPHI) set up medical information in the first place. Then the RMCPHI architecture was analyzed. Eventually, the last effective PSOSAA algorithm proposed the hospital medical information service cloud system monitoring and management application. Experimental simulation illustrates that the proposed algorithm outperforms the other state-of-the-art algorithms. Further potential research areas are discussed.

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“…As a result, several numerical discretization schemes mainly in a family of the finite difference schemes have been proposed to form a new finite difference discretization scheme. For example, the standard finite difference [18], Chebyshev finite difference [19] and Rational Finite Difference [20] are imposed for solving TPBVPs. Clearly, the development of Chebyshev finite difference and Rational Finite Difference schemes has been encouraged by the combination of the standard finite difference concept together with the Chebyshev and rational approximation functions respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Clearly, the development of Chebyshev finite difference and Rational Finite Difference schemes has been encouraged by the combination of the standard finite difference concept together with the Chebyshev and rational approximation functions respectively. In conjunction with these combinations, the author in [20] also introduced a new finite difference scheme via the combination of exponential ASTESJ ISSN: 2415-6698 approximations and finite difference discretization schemes which is known as exponential finite difference discretization schemes to show its capability for solving TPBVPs [21].…”

Section: Introductionmentioning

confidence: 99%

Redlich-Kister Finite Difference Solution for Solving Two-Point Boundary Value Problems by using Ksor Iteration Family

Suardi¹,

Sulaiman²

2021

Adv. sci. technol. eng. syst. j.

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In this paper, we are concerned to investigate the efficiency of the second-order Redlich-Kister Finite Difference (RKFD) discretization scheme together with the Four Point Explicit Group Kaudd Successive Over Relaxation (4EGKSOR) iterative method for solving twopoint boundary value problems (TPBVPs). In order to apply this block iteration to solve any linear system, firstly we discretize all derivative terms via the second-order RKFD discretization scheme over the proposed problem in order to get the second-order RKFD approximation equation. Due to the main characteristics of the coefficient matrix for the generated linear system which are large-scale and sparse, the best choice for solving this linear system is using one of the iterative methods. Therefore, the formulation of the Kaudd Successive Over Relaxation method together with the Explicit Group iteration method mainly on the Four-Point Explicit Group Kaudd Successive Over Relaxation (4EGKSOR) iterative method has been presented to solve this linear system iteratively. In order to show the efficiency of the 4EGKSOR, another two iterative methods have also been considered which are the Gauss-Seidel (GS) and the Kaudd Successive Over Relaxation (KSOR) to solve three examples of the proposed problems in which all numerical results obtained were recorded based on the number of iterations, execution time and maximum norm. Based on the performance analysis, clearly, the 4EGKSOR iterative method shows substantiated improvement in terms of the number of iterations and execution time.

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A Finite Difference Method of High Order Accuracy for the Solution of Two-Point Boundary Value Problems

Cited by 5 publications

References 16 publications

Numerical Algorithm of Block Method for General Second Order ODEs using Variable Step Size

Numerical Algorithm of Block Method for General Second Order ODEs using Variable Step Size

Combination of Cloud Computing and Internet of Things (IOT) in Medical Monitoring Systems

Redlich-Kister Finite Difference Solution for Solving Two-Point Boundary Value Problems by using Ksor Iteration Family

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