Using reproducing kernel for solving a class of singularly perturbed problems

Wang, Yulan; Su, Lijuan; Cao, Xuejun; Li, Xiaona

doi:10.1016/j.camwa.2010.11.019

Cited by 42 publications

(28 citation statements)

References 13 publications

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“…Recently, based on the reproducing kernel theory, a method called the reproducing kernel method for solving operator equations (RKM) was proposed by Geng and Cui [10], Cui and Geng [11] and Cui et al [12]. Recently, the method has been applied to many fields [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

A new numerical method for singularly perturbed turning point problems with two boundary layers based on reproducing kernel method

Geng

Qian

2016

Calcolo

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In this paper, a simple numerical method is proposed for solving singularly perturbed boundary layers problems exhibiting twin boundary layers. The method avoids the choice of fitted meshes. Firstly the original problem is transformed into a new boundary value problem whose solution does not change rapidly by a proper variable transformation; then the transformed problem is solved by using the reproducing kernel method. Two numerical examples are given to show the effectiveness of the present method.

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Section: Introductionmentioning

confidence: 99%

A new numerical method for singularly perturbed turning point problems with two boundary layers based on reproducing kernel method

Geng

Qian

2016

Calcolo

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“…Reproducing kernel theory has significant implementations in numerical analysis, differential equations, probability and statistics [18,35,37,40]. Recently, utilizing the reproducing kernel method (RKM), some authors investigated fractional differential equations, nonlinear oscillators with discontinuity, singular and nonlinear partial differential equations [1-4, 6, 7, 12-14, 16, 19, 21-28, 30-34, 36, 38, 39, 41].…”

Section: Introductionmentioning

confidence: 99%

Solutions of nonlinear systems by reproducing kernel method

Akgül¹,

Khan²,

Akgül³

et al. 2017

J. Nonlinear Sci. Appl.

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A novel approximate solution is obtained for viscoelastic fluid model by reproducing kernel method (RKM). The resulting equation for viscoelastic fluid with magneto-hydrodynamic flow is transformed to the nonlinear system by introducing the dimensionless variables. Results are presented graphically to study the efficiency and accuracy of the reproducing kernel method. Results show that this method namely RKM is an efficient method for solving nonlinear system in any engineering field.

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“…In [1][2][3][4][5][6][7][8], it is very difficult to get reproducing kernel space of problem (1). This paper is concerned with a new algorithm for giving the analytical and approximate solutions of a class of fourth-order in the new reproducing kernel space.…”

Section: Introductionmentioning

confidence: 99%

“…Many authors [9][10][11][12][13][14][15] have studied existence and uniqueness of fourth order ordinary differential equations with various boundary conditions. Recently, the reproducing kernel methods [1][2][3][4][5][6][7][8] emerge one after another. However, these reproducing kernel methods are very difficult to deal with the general conditions of determining the solution.…”

Section: Introductionmentioning

confidence: 99%