A reproducing kernel Hilbert space pseudospectral method for numerical investigation of a two-dimensional capillary formation model in tumor angiogenesis problem

Emamjome, M.; Azarnavid, Babak; Ghehsareh, Hadi Roohani

doi:10.1007/s00521-017-3184-4

Cited by 5 publications

(2 citation statements)

References 44 publications

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“…where c i and d i are the coefficients of reproducing kernel and can be determined by solving a uniquely solvable linear system of algebraic equations, which is completely explained in Cui and Lin (2009). For more details about the method of obtaining kernel K (x, y), refer to Cui and Lin (2009), Geng and Cui (2007), and Li and Cui (2003). a, b] and, therefore, it is also a reproducing kernel space.…”

Section: Multi-point Boundary Conditionmentioning

confidence: 99%

Reproducing kernel pseudospectral method for the numerical investigation of nonlinear multi-point boundary value problems

2018

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This paper presents a computational method to solve nonlinear boundary value problems with multi-point boundary conditions. These problems have important applications in the theoretical physics and engineering problems. The method is based on reproducing kernel Hilbert spaces operational matrices and an iterative technique is used to overcome the nonlinearity of the problem. Furthermore, a rigorous convergence analysis is provided and some numerical tests reveal the high efficiency and versatility of the proposed method. The results of numerical experiments are compared with analytical solutions and the best results reported in the literature to confirm the good accuracy of the presented method.

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Section: Multi-point Boundary Conditionmentioning

confidence: 99%

Reproducing kernel pseudospectral method for the numerical investigation of nonlinear multi-point boundary value problems

2018

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“…Arqub et al [6] have constructed the modulation of reproducing kernel technique successfully. Emamjome et al [7] have presented the reproducing kernel pseudospectral technique in details. Foroutan et al [8] have investigated this technique for the nonlinear three-point boundary value problems.…”

Section: Introductionmentioning

confidence: 99%

On the solutions of boundary value problems

Akgül

Hashemi

Seyfi

2021

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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We investigate the nonlinear boundary value problems by reproducing kernel Hilbert space technique in this paper. We construct some reproducing kernel Hilbert spaces. We define a bounded linear operator to obtain the solutions of the problems. We demonstrate our numerical results by some tables. We compare our numerical results with some results exist in the literature to present the efficiency of the proposed method.

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A novel application of kernel adaptive filtering algorithms for attenuation of noise interferences

Raja

Chaudhary

Ahmed

et al. 2019

Neural Comput & Applic

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A reproducing kernel Hilbert space pseudospectral method for numerical investigation of a two-dimensional capillary formation model in tumor angiogenesis problem

Cited by 5 publications

References 44 publications

Reproducing kernel pseudospectral method for the numerical investigation of nonlinear multi-point boundary value problems

Reproducing kernel pseudospectral method for the numerical investigation of nonlinear multi-point boundary value problems

On the solutions of boundary value problems

A novel application of kernel adaptive filtering algorithms for attenuation of noise interferences

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