A novel fast modification of the Adomian decomposition method to solve integral equations of the first kind with hypersingular kernels

Novin, Reza; Araghi, Mohammad Ali Fariborzi; Mahmoudi, Yaghoub

doi:10.1016/j.cam.2018.04.055

Cited by 14 publications

(9 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now, the HPM is considered to be applied to create a solution to equation (19) which is an integral equation of the second kind. To do so, consider the following…”

Section: Preliminariesmentioning

confidence: 99%

“…By employing the repeated scheme mentioned in equation (39) we now illustrate that where fðyÞ ¼ 4y refers to a polynomial of order one, then plugging the HPM in equation 76, and considering equation (19) and equation (27) we get the following…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…where fðyÞ ¼ 8y 3 À 2y þ 1 refers to a polynomial of 3, then plugging the HPM in equation 95, and considering equation (19) and equation (27), so equation (96) would be as follows…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…Obviously, in the case of evaluating the approximate solution of the hypersingular integral equations, plenty of methods need to be prepared. [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] To improve a solution to a general hypersingular integral equation of the first kind, one simple but precise approximation method is chosen and investigated in Mandal and Bera. 34 Consideration should be given to the kernel which should be divided to hypersingular and regular parts.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Hypersingular integral equations of the first kind: A modified homotopy perturbation method and its application to vibration and active control

Novin

Araghi

2019

Journal of Low Frequency Noise, Vibration and Active Control

Self Cite

View full text Add to dashboard Cite

This paper attempts to propose and investigate a modification of the homotopy perturbation method to study hypersingular integral equations of the first kind. Along with considering this matter, of course, the novel method has been compared with the standard homotopy perturbation method. This method can be conveniently fast to get the exact solutions. The validity and reliability of the proposed scheme are discussed. Different examples are included to prove so. According to the results, we further state that new simple homotopy perturbation method is so efficient and promises the exact solution. The modification of the homotopy perturbation method has been discovered to be the significant ideal tool in dealing with the complicated function-theoretic analytical structures within an analytical method.

show abstract

“…Now, the HPM is considered to be applied to create a solution to equation (19) which is an integral equation of the second kind. To do so, consider the following…”

Section: Preliminariesmentioning

confidence: 99%

Section: Illustrative Examplesmentioning

confidence: 99%

“…where fðyÞ ¼ 8y 3 À 2y þ 1 refers to a polynomial of 3, then plugging the HPM in equation 95, and considering equation (19) and equation (27), so equation (96) would be as follows…”

Section: Illustrative Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Hypersingular integral equations of the first kind: A modified homotopy perturbation method and its application to vibration and active control

Novin

Araghi

2019

Journal of Low Frequency Noise, Vibration and Active Control

Self Cite

View full text Add to dashboard Cite

show abstract

“…A large class of problems in such fields have been described by autonomous Duffing-and Liénard-type ordinary differential equations (ODE). Consequently, getting exact or accurate closed-form approximate solutions for such equations has been a topic of intense research for many years Since its inception, Adomian decomposition method (ADM) has been used to get an approximate solution of nonlinear differential/integral equations in the diverse field of science and engineering [26][27][28][29][30][31]. However, one of its important aspects, e.g.…”

Section: Introductionmentioning

confidence: 99%

Some modifications on RCAM for getting accurate closed-form approximate solutions of Duffing- and Lienard-type equations

Das

Singh

Panja

2019

JAM

View full text Add to dashboard Cite

In this work, authors propose some modifications Adomian decomposition method to get some accurate closed form approximate or exact solutions of Duffing- and Li´enard-type nonlinear ordinary differential equations.Results obtained by the revised scheme have been exploited subsequently to derive constraints among parameters to get the solutions to be bounded. The present scheme appears to be efficient and may be regarded as the confluence of apparently different methods for getting exact solutions for a variety of nonlinear ordinary differential equations appearing as mathematical models in several physical processes.

show abstract

Superconvergence results for hypersingular integral equation of first kind by Chebyshev spectral projection methods

Gupta,

Kayal,

Mandal

2025

Applied Mathematics and Computation

View full text Add to dashboard Cite

A novel fast modification of the Adomian decomposition method to solve integral equations of the first kind with hypersingular kernels

Cited by 14 publications

References 20 publications

Hypersingular integral equations of the first kind: A modified homotopy perturbation method and its application to vibration and active control

Hypersingular integral equations of the first kind: A modified homotopy perturbation method and its application to vibration and active control

Some modifications on RCAM for getting accurate closed-form approximate solutions of Duffing- and Lienard-type equations

Superconvergence results for hypersingular integral equation of first kind by Chebyshev spectral projection methods

Contact Info

Product

Resources

About