Legendre multi-wavelets collocation method for numerical solution of linear and nonlinear integral equations

Asif, Muhammad; Khan, Imran; Haider, Nadeem; Al‐Mdallal, Qasem M.

doi:10.1016/j.aej.2020.09.040

Cited by 23 publications

(8 citation statements)

References 37 publications

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“…The presence of NLBC makes such a problem applicable when modeling processes such as blood ow, underground water ow, population dynamics, and thermo-elasticity. We can also extend this work in fractional calculus for NLBC [14,18,2,3,4,6,7,15].…”

Section: Introductionmentioning

confidence: 95%

An Efficient Numerical Technique for Solving Heat Equation With Nonlocal Boundary Conditions

Hammouch

ZAHRA

Rehman³

et al. 2022

Advances in the Theory of Nonlinear Analysis and Its Application

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A fourth order parallel splitting algorithm is proposed to solve one dimensional non-homogeneous heat equation with integral boundary conditions. we approximate the space derivative by fourth order nite dierence approximation. This parallel splitting technique is combined with Simpson's 1/3 rule to tackle nonlocal part of this problem. The algorithm develop here is tested on two model problems. We conclude that our method provides better accuracy due to availability of real arithmetic.

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Section: Introductionmentioning

confidence: 95%

An Efficient Numerical Technique for Solving Heat Equation With Nonlocal Boundary Conditions

Hammouch

ZAHRA

Rehman³

et al. 2022

Advances in the Theory of Nonlinear Analysis and Its Application

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“…Deniz in [12] has used a modification of the optimal perturbation iteration method to solve the nonlinear VIEs. Next, Linear and nonlinear IEs have been solved by Legendre multi-wavelets collocation method in [13]. Sathar et al [14] presented a numerical technique based on a mix of Haar Wavelets Methods and Newton-Kantorovich to solve second kind nonlinear Volterra-Fredholm IEs.…”

Section: Introductionmentioning

confidence: 99%

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2022

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“…In this work, we implement the haar wavelet method for the solution of eight order boundary value problems. It is worthy mentioning that the Haar wavelet method has been used recently to solve different classes of integral and differential equations; see for example [ 7 – 9 ].…”

Section: Introductionmentioning

confidence: 99%

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

Amin

Shah

Al‐Mdallal

et al. 2021

Int. J. Appl. Comput. Math

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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.

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Legendre multi-wavelets collocation method for numerical solution of linear and nonlinear integral equations

Cited by 23 publications

References 37 publications

An Efficient Numerical Technique for Solving Heat Equation With Nonlocal Boundary Conditions

An Efficient Numerical Technique for Solving Heat Equation With Nonlocal Boundary Conditions

Untitled

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

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