Spline collocation method for solving linear sixth-order boundary-value problems

Lamnii, A.; Mraoui, H.; Sbibih, D.; Tijini, A.; Zidna, Ahmed

doi:10.1080/00207160701543392

Cited by 17 publications

(17 citation statements)

References 8 publications

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“…Equation (46) is a family of the approximate solutions to problem (14) in terms of the convergence control parameter ℎ.…”

Section: (37)mentioning

confidence: 99%

“…We choose the value of auxiliary parameter as ℎ = −1 to ensure that the solution series converges. For problem (14), comparison of the results of the present method with the results of Akram and Rehman [9], Inc and Evans [7], and Siddiqi and Akram [5] is shown in Table 4. It is observed that the errors in absolute values of the present method are better.…”

Section: (37)mentioning

confidence: 99%

“…Siddiqi and Twizell [13] presented the solutions of tenth-order boundary value problems using tenth degree spline, where some unexpected results, for the solution and higher order derivatives, were obtained near the boundaries of the interval. Lamnii et al [14] developed a spline collocation method using spline interpolants and analyzed the approximating solutions of some general linear boundary value problems. Domairry and Nadim in [15] compared the HAM and HPM in solving nonlinear heat transfer equation.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Solution of Higher Order Boundary Value Problems

Siddiqi

Iftikhar

2013

Abstract and Applied Analysis

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The aim of this paper is to use the homotopy analysis method (HAM), an approximating technique for solving linear and nonlinear higher order boundary value problems. Using HAM, approximate solutions of seventh-, eighth-, and tenth-order boundary value problems are developed. This approach provides the solution in terms of a convergent series. Approximate results are given for several examples to illustrate the implementation and accuracy of the method. The results obtained from this method are compared with the exact solutions and other methods (Akram and Rehman (2013), Farajeyan and Maleki (2012), Geng and Li (2009), Golbabai and Javidi (2007), He (2007), Inc and Evans (2004), Lamnii et al. (2008), Siddiqi and Akram (2007), Siddiqi et al. (2012), Siddiqi et al. (2009), Siddiqi and Iftikhar (2013), Siddiqi and Twizell (1996), Siddiqi and Twizell (1998), Torvattanabun and Koonprasert (2010), and Kasi Viswanadham and Raju (2012)) revealing that the present method is more accurate.

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“…Equation (46) is a family of the approximate solutions to problem (14) in terms of the convergence control parameter ℎ.…”

Section: (37)mentioning

confidence: 99%

Section: (37)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical Solution of Higher Order Boundary Value Problems

Siddiqi

Iftikhar

2013

Abstract and Applied Analysis

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“…x ) x ( y Table 3 bellow exhibits the numerical results and the errors obtained by using the differential transform method (DTM) with comparison to the exact solution. The analytical solution of the above problem [12] is:…”

Section: Solutionmentioning

confidence: 99%

Solution of Eighth Order Boundary Value Problems Using Differential Transformation Technique

Samarchi¹

2010

AL-Rafidain Journal of Computer Sciences and Mathematics

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In this paper we have applied the Differential Transform Method (DTM) for solving eighth-order boundary value problems. The analytical and numerical results of the equations have been obtained in terms of convergent series with the easily computable components. Three examples are considered for the numerical illustrate and implementation of this method. Numerical Comparisons with respect to the analytical solutions have been considered . It is observed that the method is an alternative and efficient for finding the approximate solutions of the boundary values problems. Key Words: Differential Transform Method, boundary value problems, analytical solution ‫التفاضلي‬ ‫التحويل‬ ‫طريقة‬ ‫باستخدام‬ ‫الثامنة‬ ‫الرتبة‬ ‫من‬ ‫الحدودية‬ ‫القيم‬ ‫مسائل‬ ‫حل‬ ‫عزيز‬ ‫عادل‬ ‫ميرنا‬ ‫الرياضيات‬ ‫و‬ ‫الحاسوب‬ ‫علوم‬ ‫كلية‬ ، ‫الموصل‬ ‫جامعة‬ ‫البحث‬ ‫استالم‬ ‫تاريخ‬ : 28 / 9 / 2009 ‫البحث‬ ‫قبول‬ ‫تاريخ‬ : 21 / 2 / 2010 ‫الملخص‬ ‫استخدا‬ ‫البحث‬ ‫هذا‬ ‫في‬ ‫تم‬ ‫تبة‬ ‫الر‬ ‫من‬ ‫الحدودية‬ ‫القيم‬ ‫مسائل‬ ‫لحل‬ ‫التفاضلي‬ ‫التحويل‬ ‫يقة‬ ‫طر‬ ‫م‬ ‫ـة‬ ‫ب‬ ‫متقار‬ ‫متسلسالت‬ ‫خالل‬ ‫من‬ ‫للمعادالت‬ ‫العددية‬ ‫و‬ ‫التحليلية‬ ‫النتائج‬ ‫على‬ ‫الحصول‬ ‫تم‬ ‫وقد‬ ‫الثامنة،‬ ‫وتوضيح‬ ‫يقة‬ ‫الطر‬ ‫لتطبيق‬ ‫أمثلة‬ ‫ثالث‬ ‫البحث‬ ‫تضمن‬ ‫ـة.‬ ‫سهل‬ ‫حسابية‬ ‫بطرق‬ ‫محددة‬ ‫معامالت‬ ‫ذات‬ ‫التحليل‬ ‫الحلول‬ ‫مع‬ ‫يقة‬ ‫الطر‬ ‫وم‬ ‫ية‬ ‫ن‬ ‫هذه‬ ‫ـالل‬ ‫خ‬ ‫لهذه‬ ‫يت‬ ‫أجر‬ ‫قد‬ ‫العددية‬ ‫نات‬ ‫المقار‬ ‫العددية.‬ ‫نتائجها‬ ‫هذه.‬ ‫الحدودية‬ ‫القيم‬ ‫لمسائل‬ ‫يبية‬ ‫التقر‬ ‫الحلول‬ ‫ـاد‬ ‫إيج‬ ‫في‬ ‫يقة‬ ‫الطر‬ ‫هذه‬ ‫وكفاءة‬ ‫ـة‬ ‫دق‬ ‫تبين‬ ‫نات‬ ‫المقار‬ ‫المفتاحية‬ ‫الكلمات‬ ‫التحليلي‬ ‫الحل‬ ‫الحدودية,‬ ‫القيم‬ ‫مسائل‬ ‫التفاضلي,‬ ‫التحويل‬ ‫يقة‬ ‫طر‬ : .

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“…Also Siddiqi and Akram [10] used septic splines to solve the boundary value problems of type (1)-(2). Lamini et al [11] used spline collocation method to solve the sixth-order boundary value problems.…”

Section: Introductionmentioning

confidence: 99%

Cubic B-Spline Collocation Method for Sixth Order Boundary Value Problems

2017

International Journal of Scientific and Innovative Mathematical

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Spline collocation method for solving linear sixth-order boundary-value problems

Cited by 17 publications

References 8 publications

Numerical Solution of Higher Order Boundary Value Problems

Numerical Solution of Higher Order Boundary Value Problems

Solution of Eighth Order Boundary Value Problems Using Differential Transformation Technique

Cubic B-Spline Collocation Method for Sixth Order Boundary Value Problems

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