A quartic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si13.gif" display="inline" overflow="scroll"><mml:mi>B</mml:mi></mml:math>-spline for second-order singular boundary value problems

Goh, Joan; Majid, Ahmad Abd.; Ismail, Ahmad Izani Md.

doi:10.1016/j.camwa.2012.01.022

Cited by 34 publications

(7 citation statements)

References 18 publications

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“…where V k and v k (x) are used for approximate and exact solutions respectively. Moreover, the numerical results are compared with CPCBSM [2], cubic basis spline method (CBSM) [4], extended cubic B-spline method (ECBM) [10], quartic B-spline method (QBSM) [11], new CBSM (NCBSM) [12], variational iteration method (VIM) [26], Green's functions associated with improved form of Adomian decomposition method (GIADM) [30], adomian decomposition method (ADM) [31], semi numerical method (SNM) [31], RKM [33], and IDTM [35]. The resulting equation is also known as Bessel's equation of order zero.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…The resulting equation is also known as Bessel's equation of order zero. In Table 1, the error norms obtained by the proposed method are compared with the CBSM [4], EBSM [10], and QBSM [11] using three choices of h. For h = 0.1, 0.05, 0.02, the values σ = −0.005812, −0.00066, −0.000011 have been used respectively. It is observed that the obtained results are more accurate in comparison to other methods.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…The analytic solution for this problem is v(x) = J 0 (x) J 0 (1) . CBSM [4] ECBSM [10] QBSM [11] Proposed method h…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…The accuracy of the proposed numerical scheme has been enhanced by means of a new approximation for 2 nd order derivative. The computational results are compared with those obtained by CPCBSM [2], CBSM [4], ECBSM [10], QBSM [11], NCBSM [12], VIM [26], GIADM [30], ADM [31], SNM [31], RKM [33], and IDTM [35]. It is concluded that the presented algorithm has very simple implementation and produces more accurate outcomes as compared to existing numerical techniques.…”

Section: Discussionmentioning

confidence: 97%

“…Abukhaled et al [2] used B-spline functions with chebyshev polynomials (CPCBSM) for solving SBVPs. Goh et al [10,11] investigated the approximate solution of linear SBVPs with the help of quartic and extended uniform B-spline functions. The authors in [14], proposed a new quartic B-spline approximation technique for numerical investigation of third order SBVPs.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A new extended B-spline approximation technique for second order singular boundary value problems arising in physiology

Wasim¹,

Abbas²,

Iqbal³

2019

J. Math. Computer Sci.

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In this study, we have explored the approximate solution of 2 nd order singular boundary value problems (SBVP's) using extended cubic B-spline (ECBS) collocation approach. The accuracy of the numerical algorithm has been enhanced by means of a novel ECBS approximation for 2 nd order derivative. To endorse our claim, few test examples have been considered and the experimental results are compared with the already existing methods. It is observed that the proposed technique is more accurate and efficient in comparison to the existing techniques on the topic.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…The analytic solution for this problem is v(x) = J 0 (x) J 0 (1) . CBSM [4] ECBSM [10] QBSM [11] Proposed method h…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A new extended B-spline approximation technique for second order singular boundary value problems arising in physiology

Wasim¹,

Abbas²,

Iqbal³

2019

J. Math. Computer Sci.

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An optimal sixth‐order quartic B‐spline collocation method for solving Bratu‐type and Lane‐Emden–type problems

Roul

Thula

Goura

2019

Math Methods in App Sciences

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This paper is concerned with the numerical solutions of Bratu‐type and Lane‐Emden–type boundary value problems, which describe various physical phenomena in applied science and technology. We present an optimal collocation method based on quartic B‐spine basis functions to solve such problems. This method is constructed by perturbing the original problem and on a uniform mesh. The method has been tested by four nonlinear examples. In order to show the advantage of the new method, numerical results are compared with those obtained by some of the existing methods, such as normal quartic B‐spline collocation method and the finite difference method (FDM). It has been observed that the order of convergence of the proposed method is six, which is two orders of magnitude larger than the normal quartic B‐spline collocation method. Moreover, our method gives highly accurate results than the FDM.

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A high‐order efficient technique and its convergence analysis for Bratu‐type and Lane‐Emden‐type problems

Roul

Goura

2022

Math Methods in App Sciences

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The present work deals with the construction of a high‐order efficient technique for solving one‐dimensional nonlinear Bratu‐type and Lane‐Emden‐type problems describing various physical, chemical and biological phenomena in applied science and engineering. Convergence analysis of the method is studied. Numerical experiments are carried out to demonstrate the efficiency, accuracy and performance of proposed method. The method is shown to have sixth order convergence. The computed results are compared with those obtained by other numerical techniques to justify the advantage of present scheme. It is shown that the proposed method is fast convergent and provides accurate solutions for Bratu‐type and Lane‐Emden‐type problems with low computational cost.

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A quartic B-spline for second-order singular boundary value problems

Cited by 34 publications

References 18 publications

A new extended B-spline approximation technique for second order singular boundary value problems arising in physiology

A new extended B-spline approximation technique for second order singular boundary value problems arising in physiology

An optimal sixth‐order quartic B‐spline collocation method for solving Bratu‐type and Lane‐Emden–type problems

A high‐order efficient technique and its convergence analysis for Bratu‐type and Lane‐Emden‐type problems

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