Numerical approach for the solution of hypersingular integro-differential equations

Gülsu, Mustafa; Öztürk, Yalçın

doi:10.1016/j.amc.2013.12.163

Cited by 7 publications

(5 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By using the expression (5) and (6) and taking N r , , 1 , 0 ! = we find the corresponding matrix relation as follows…”

Section: Fundamental Matrix Relationsmentioning

confidence: 99%

See 1 more Smart Citation

Chebyshev series solution for a class system of linear integro-differential equations with weakly singular kernel

Öztürk

2019

Adıyaman University Journal of Science

Self Cite

View full text Add to dashboard Cite

In this study, a numerical algorithm for solving a class of system of linear integro differential equations with weakly singular kernel is presented. This algorithm is based on polynomial approximation and collocation method, using the first kind Chebyshev polynomial basis. This method transforms the equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. To show the validity and applicability of the numerical method some experiments are examined.Present method is compared some numerical methods. ÖzBu çalışmada, zayıf tekil çekirdekli lineer integro diferansiyel denklemlerin bir sınıfı için bir nümerik algoritma sunulacaktır. Bu algoritma birinci tip Chebyshev polinom bazı yardımıyla polinom yaklaşımı ve sıralama metodunu temel almaktadır. Bu metot verilen denklem ve koşulları bir matris denklemine dönüştürür. Nümerik metodun uygulanabilirliğini ve doğruluğunu göstermek amacıyla bazı örnekler incelenecektir.Sunulan metot diğer metotlar ile kıyaslanmıştır.

show abstract

“…By using the expression (5) and (6) and taking N r , , 1 , 0 ! = we find the corresponding matrix relation as follows…”

Section: Fundamental Matrix Relationsmentioning

confidence: 99%

“…These type equations have been solved numerically by some authours. We can give some studies in literature [5][6][7][8][9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Chebyshev series solution for a class system of linear integro-differential equations with weakly singular kernel

Öztürk

2019

Adıyaman University Journal of Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…In certain cases, there exist some analytical methods for solving HSIEs, but in general, there is no known analytical method. Thus, different numerical methods are introduced and developed for solving HSIEs [8,9,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

A Novel Collocation Method for Numerical Solution of Hypersingular Integral Equation with Singular Right-Hand Function

Elahi

Mahmoudi

Shamloo

et al. 2023

Advances in Mathematical Physics

View full text Add to dashboard Cite

In this study, the Fredholm hypersingular integral equation of the first kind with a singular right-hand function on the interval − 1 , 1 is solved. The discontinuous solution on the domain − 1 , 1 is approximated by a piecewise polynomial, and a collocation method is introduced to evaluate the unknown coefficients. This method, which can be applied to both linear and nonlinear integral equations, is very simple and straightforward. The presented illustrations relate that the results are very accurate compared to the other methods in the literature.

show abstract

“…There exist lots of literature on related applications of semi-analytical and numerical methods for hypersingular integral equation (1) on its special case K(x, s) = 1 and L(x, s) = 0. The applied methods involve projection method [10], polynomial approximation method [5,11], Bernestein polynomials approximation method [6], Spline collocation method [12,13], Chebyshev polynomials approximation methods [14,15], modified Adomian decomposition method [16,17] and new homotopy perturbation method [18].…”

Section: Introductionmentioning

confidence: 99%

On projection method for numerical solution of hypersingular integral equations of the first kind combined with quadrature methods

et al. 2023

View full text Add to dashboard Cite

The Fredholm integral equations of the ﬁrst kind with two regular and hypersingular kernels are considered on [−1, 1]. The hypersingular kernel is considered smooth enough with no additional conditions. A projection method based on second kind Chebyshev polynomials approximation, combined with quadrature integration method, is developed to obtain high accurate approximations. The proposed method reduces the underlying integral equation to a system of algebraic equations. Several illustrative examples are provided to show the eﬃciency of the method.

show abstract

Numerical approach for the solution of hypersingular integro-differential equations

Cited by 7 publications

References 10 publications

Chebyshev series solution for a class system of linear integro-differential equations with weakly singular kernel

Chebyshev series solution for a class system of linear integro-differential equations with weakly singular kernel

A Novel Collocation Method for Numerical Solution of Hypersingular Integral Equation with Singular Right-Hand Function

On projection method for numerical solution of hypersingular integral equations of the first kind combined with quadrature methods

Contact Info

Product

Resources

About