Efficient Numerical Algorithm for the Solution of Eight Order Boundary Value Problems by Haar Wavelet Method

被引：10

作者：

Amin R. ^{[1
]}

Shah K. ^{[2
]}

Al-Mdallal Q.M. ^{[3
]}

Khan I. ^{[1
]}

Asif M. ^{[1
]}

机构：

[1] Department of Mathematics, University of Peshawar, Peshawar, 25120, Khyber Pakhtunkhwa

[2] Department of Mathematics, University of Malakand, Dir(L), 18000, Khyber Pakhtunkhwa

[3] Deparment of Mathematical Sciences, United Arab Emirates University, P.O Box 15551, Al Ain, Abu Dhabi

来源：

International Journal of Applied and Computational Mathematics | 2021年 / 7卷 / 2期

关键词：

Boundary value problems; Collocation method; Gauss elimination method; Haar wavelet;

D O I：

10.1007/s40819-021-00975-x

中图分类号：

学科分类号：

摘要：

In this paper, the Haar technique is applied to both nonlinear and linear eight-order boundary value problems. The eight-order derivative in the boundary value problem is approximated using Haar functions in this technique and the integration process is used to obtain the expression of the lower order derivative and the approximate solution of the unknown function. For the verification of validation and convergence of the proposed technique, three linear and two nonlinear examples are taken from the literature. The results are also compared with other methods available in the literature. Maximum absolute and root mean square errors at various collocation and Gauss points are contrasted with the exact solution. The convergence rate is also measured, which is almost equivalent to 2, using different numbers of collocation points. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited part of Springer Nature.

引用

共 32 条

[1]

Chandrasekhar S., Hydrodynamic and Hydromagnetic Stability, (1961)

[2]

Bishop R.E.D., Cannon S.M., Miao S., On coupled bending and torsional vibration of uni-form beams, J. Sound Vib., 131, pp. 309-325, (1989)

[3]

Akram G., Siddiqi S., Nonic spline solutions of eighth order boundary value problems Appl, Math. Comput., 182, pp. 829-845, (2006)

[4]

Siddiqi S., Akram G., Solution of eighth-order boundary value problems using the non-polynomial spline technique, Int. J. Comput. Math., 182, pp. 347-368, (2007)

[5]

Wazwaz A.M., The numerical solutions of special eighth-order boundary value problems by the modified decomposition method, Neural Parallel Sci. Comput., 8, pp. 133-146, (2000)

[6]

Siddiqi S.S., Twizell E.H., Spline solutions of linear eighth-order boundary-value problems, Comput. Methods Appl. Mech. Eng., 131, pp. 457-464, (1996)

[7]

Asif M., Haider N., Al-Mdallal Q.M., Khan I., A Haar wavelet collocation approach for solving one and two-dimensional second-order linear and nonlinear hyperbolic telegraph equations, Numer. Methods Partial Differ. Equ., 36, 6, pp. 1962-1981, (2020)

[8]

Abdeljawad T., Amin R., Shah K., Al-Mdallal Q.M., Jarad F., Efficient sustainable algorithm for numerical solutions of systems of fractional order differential equations by Haar wavelet collocation method, Alex. Eng. J., 59, 4, pp. 2391-2400, (2020)

[9]

Asif M., Khan I., Haider N., Al-Mdallal Q.M., Legendre multi-wavelets collocation method for numerical solution of linear and nonlinear integral equations, Alex. Eng. J., 59, 6, pp. 5099-5109, (2020)

[10]

Boutayeb A., Twizell E.H., Finite-difference methods for the solution of special eighth-order boundary-value problems, Int. J. Comput. Math., 48, pp. 63-75, (1993)

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