The Coiflet–Galerkin method for linear Volterra integral equations

Saberi‐Nadjafi, Jafar; Mehrabinezhad, Mohammad; Diogo, Teresa

doi:10.1016/j.amc.2013.06.100

Cited by 5 publications

(5 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…are obtained in comparison with Coiflet-Galerkin method (n=6) [21]. We apply the present method to solve this equation by taking N from 4 to 12.…”

Section:  mentioning

confidence: 99%

“…This consistence is also seen in Figure 3. [20,21] Consider the Volterra integral equation with functional kernel…”

Section:  mentioning

confidence: 99%

“…In recent years, integral equations have been encountered in variety applied sciences, such as mathematics, engineering, thermodynamic, molecular properties, electromagnetics, Stokes flow, heat and mass transfer, and micromechanics [1][2][3][4][5][16][17][18][19][20][21]. Most of the time, integral equations and their different types are too hard to be solved analytically.…”

Section: Introductionmentioning

confidence: 99%

“…Also, in order to solve the Volterra integral equations for the second kind, Adomian's decomposition method has been employed by Babolian and Davary [16]. Variational iteration method, collocation method, Walsh functions method and Coiflet-Galerkin method have been introduced to solve the integral equations and their some types [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A New Numerical Method for Solving Functional Delay Integral Equations With Variable Bounds by Using Generalized Mott Polynomials

Kürkçü¹

2018

Anadolu University Journal of Science and Technology-a Applied Sciences and Engineering

View full text Add to dashboard Cite

In this study, the delay integral equations with variable bounds are considered and their approximate solutions are obtained by using a new numerical method based on matrices, collocation points and the generalized Mott polynomials including a parameter-. An error analysis technique consisting of the residual function is performed. The numerical examples are applied to illustrate the practicability and usability of the method. The behavior of the solutions is monitored in terms of the parameter-. The accuracy of the method is scrutinized for different values of N and also the numerical results are discussed in figures and tables.

show abstract

“…are obtained in comparison with Coiflet-Galerkin method (n=6) [21]. We apply the present method to solve this equation by taking N from 4 to 12.…”

Section:  mentioning

confidence: 99%

“…This consistence is also seen in Figure 3. [20,21] Consider the Volterra integral equation with functional kernel…”

Section:  mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A New Numerical Method for Solving Functional Delay Integral Equations With Variable Bounds by Using Generalized Mott Polynomials

Kürkçü¹

2018

Anadolu University Journal of Science and Technology-a Applied Sciences and Engineering

View full text Add to dashboard Cite

show abstract

“…Similar approaches of Chebyshev wavelet collocation method [9] and Haar wavelet collocation method [10] were used to solve this kind of integral equations. The continuous wavelet Galerkin method [11] and the Coiflet-Galerkin method [12] were proposed for the second kind integral equations and linear Volterra integral equations, respectively. Ren et al [13] applied the Taylor polynomial method for a class of second kind integral equations.…”

Section: Introductionmentioning

confidence: 99%

A New Wavelet Method for Solving a Class of Nonlinear Volterra-Fredholm Integral Equations

Wang

2014

Abstract and Applied Analysis

View full text Add to dashboard Cite

A new approach, Coiflet-type wavelet Galerkin method, is proposed for numerically solving the Volterra-Fredholm integral equations. Based on the Coiflet-type wavelet approximation scheme, arbitrary nonlinear term of the unknown function in an equation can be explicitly expressed. By incorporating such a modified wavelet approximation scheme into the conventional Galerkin method, the nonsingular property of the connection coefficients significantly reduces the computational complexity and achieves high precision in a very simple way. Thus, one can obtain a stable, highly accurate, and efficient numerical method without calculating the connection coefficients in traditional Galerkin method for solving the nonlinear algebraic equations. At last, numerical simulations are performed to show the efficiency of the method proposed.

show abstract