Numerical solution of third order boundary value problems using one-step hybrid block method

Abdelrahim, Ra’ft

doi:10.1016/j.asej.2018.02.003

Cited by 8 publications

(8 citation statements)

References 3 publications

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“…The efficiency curve shows that S3HI3 performed better in terms of error than S3HI1 and S3HI3 which have slightly better CPU time than S3HI2. Table 2 shows errors obtain for Problem 2 with h = 0.1 using the methods S3HI1, S3HI2, S3HI3 and a method of order 8 in [12]. The table agrees with the efficiency curve which indicate that S3HI1 and S3HI3 have the same performance while S3HI2 performed better when compared to its counterparts and the method of order 7 in [12].…”

Section: Numerical Test Problems and Resultssupporting

confidence: 65%

“…The proposed S3HI1, S3HI2, S3HI3 performed well in terms of error and time as such, they out performed S3BHM and OSTEM in terms of accuracy and time cost. Table 4 shows the maximum error obtained using different step-sizes and compared with the an order 7 method in [12]. It clearly shows that S3HI1, S3HI2 and S3HI3 are almost equivalent in performance but more superior to the method cited.…”

Section: Numerical Test Problems and Resultsmentioning

confidence: 94%

“…. , N. For the solution of (1) with initial condition, the method proposed in [12], three off-step points in the interval 0 < x r < x s < x t < 1 are given such that (r, s, t) = ( 3 8 , 5 8 , 7 8 ). Also, an optimized two-step method with three off-step points proposed in [13] is such that r, s, v are in the interval 0 < r, s, t < 2.…”

Section: Derivation Of the Methodsmentioning

confidence: 99%

“…. Consider the BVP discussed in[12].y + y = (x − 4) sin(x) + (1 − x) cos(x), x ∈ [0, 1] y(0) = 0, y (0) = 1, y (1) = − sin 1 (31)whose exact solution is y(x) = (x − 1) sin(x).…”

mentioning

confidence: 99%

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Computational study of a 3-step hybrid integrators for third order ordinary differential equations with shift of three off-step points

Modebei¹,

Olaiya²,

Ngwongwo

2021

J. Nig. Soc. Phys. Sci.

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A Block of hybrid method with three off-step points based is presented in this work for direct approximation of solution of third-order Initial and Boundary Value Problems (IVPs and BVPs). This off-step points are formulated such that they exist only on a single step at a time. Hence, these points are shifted to three positions respectively in order to obtain three different integrators for computational analysis. These analysis includes; order of the methods, consistency, stability and convergence, global error, number of functions evaluation and CPU time. The superiority of these methods over existing methods is established numerically on different test problems in literature

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Section: Numerical Test Problems and Resultssupporting

confidence: 65%

Section: Numerical Test Problems and Resultsmentioning

confidence: 94%

Section: Derivation Of the Methodsmentioning

confidence: 99%

“…. Consider the BVP discussed in[12].y + y = (x − 4) sin(x) + (1 − x) cos(x), x ∈ [0, 1] y(0) = 0, y (0) = 1, y (1) = − sin 1 (31)whose exact solution is y(x) = (x − 1) sin(x).…”

mentioning

confidence: 99%

See 2 more Smart Citations

Computational study of a 3-step hybrid integrators for third order ordinary differential equations with shift of three off-step points

Modebei¹,

Olaiya²,

Ngwongwo

2021

J. Nig. Soc. Phys. Sci.

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“…Although, a huge number of different methods have been used previously for some linear and nonlinear differential problems, there is still need to construct methods which are accurate and of low computational cost for solutions of dynamic obstacles. The solution of these types of physical problems, one-step hybrid block method has been numerically applied by Abdelrahim et al [1] to solve the third order differential problems and results signified that this developed scheme is capable to generate better outcomes while comparable to previous literature. Homotopy type techniques such as OHAM and HPM are applied for solution of higher order BVPs by Naeem et al [35].…”

Section: Introductionmentioning

confidence: 96%

Semi-analytical solutions for the hydrodynamic stability based nonlinear fourteenth order differential problem

2021

Punjab Univ. j. math.

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This research article is concerned with the solution of hydrodynamic stability based linear and nonlinear fourteenth order differential problem, which has great significance in applied physics, astrophysics, applied mathematics, engineering departments. The homotopy perturbation method (HPM) and optimal homotopy asymptotic method (OHAM) are applied for the solution of the existed problem. These semi analytical techniques are continuously evolved to solve diverse range of linear and nonlinear problems with effective approximate agents which is a rapid approach to the exact solutions. This approach is effectively proposed with different numerical examples, which are taken from literature. Numerical results are accomplished by phrase of convergent series solutions and approach to the accurate solutions only by taking minimum steps. The numerical results are exercised with exact solutions, cubic polynomial spline technique (CPST) and cubic non-polynomial spline technique (CNPST), excellent agreement has been observed. The observations suggested that OHAM and HPM performed excellent in comparison to the CPST and CNPST in terms of solution, which demonstrated the effectiveness, potential and validity of suggested schemes in reality and acquired results are of top-level perfection.

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Taylor series solution for a third order boundary value problem arising in Architectural Engineering

2020

Ain Shams Engineering Journal

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Numerical solution of third order boundary value problems using one-step hybrid block method

Cited by 8 publications

References 3 publications

Computational study of a 3-step hybrid integrators for third order ordinary differential equations with shift of three off-step points

Computational study of a 3-step hybrid integrators for third order ordinary differential equations with shift of three off-step points

Semi-analytical solutions for the hydrodynamic stability based nonlinear fourteenth order differential problem

Taylor series solution for a third order boundary value problem arising in Architectural Engineering

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