An efficient numerical technique for the solution of nonlinear singular boundary value problems

Singh, Randhir; Kumar, Jitendra

doi:10.1016/j.cpc.2014.01.002

Cited by 90 publications

(79 citation statements)

References 39 publications

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“…The maximum absolute error in the DDHPM result is given in Table 2 along with comparisons with the results obtained by the standard HPM 14 and the MADM. 20 We see that the DDHPM shows its superiority over these 2 methods as expected. The results of errors for n = 6, 8 are also plotted in Figure 2.…”

Section: Examplesupporting

confidence: 77%

On the numerical solution of singular two‐point boundary value problems: A domain decomposition homotopy perturbation approach

Roul

2017

Math Methods in App Sciences

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This paper reports a modified homotopy perturbation algorithm, called the domain decomposition homotopy perturbation method (DDHPM), for solving two-point singular boundary value problems arising in science and engineering. The essence of the approach is to split the domain of the problem into a number of nonoverlapping subdomains. In each subdomain, a method based on a combination of HPM and integral equation formalism is implemented. The boundary condition at the right endpoint of each inner subdomain is established before deriving an iterative scheme for the components of the solution series. The accuracy and efficiency of the DDHPM are demonstrated by 4 examples (2 nonlinear and 2 linear). In comparison with the traditional HPM, the proposed domain decomposition HPM is highly accurate. KEYWORDS homotopy perturbation method, isothermal gas sphere, singular boundary value problem, thermal explosion problem 7396

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Section: Examplesupporting

confidence: 77%

On the numerical solution of singular two‐point boundary value problems: A domain decomposition homotopy perturbation approach

Roul

2017

Math Methods in App Sciences

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“…The numerical study of singular boundary value problems arising in various physical models has been done by many authors [1][2][3][4][5][6][7][8][9][10][11] and a variety of methods have been introduced to solve such singular boundary B G. Hariharan hariharang2011@gmail.com 1 Department of Mathematics, School of Humanities and Sciences, SASTRA University, Thanjavur, Tamilnadu 613 401, India value problems [2,3,5,[8][9][10]. Although, these numerical methods have many advantages, but a huge amount of computational work is needed.…”

Section: Introductionmentioning

confidence: 99%

An efficient wavelet based spectral method to singular boundary value problems

Rajaraman

Hariharan

2015

J Math Chem

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In this paper, we have established an efficient wavelet based approximation method to nonlinear singular boundary value problems. To the best of our knowledge, until now there is no rigorous shifted second kind Chebyshev wavelet (S2KCWM) solution has been addressed for the nonlinear differential equations in population biology. With the help of shifted second kind Chebyshev wavelets operational matrices, the nonlinear differential equations are converted into a system of algebraic equations. The convergence of the proposed method is established. The power of the manageable method is confirmed. Finally, we have given some numerical examples to demonstrate the validity and applicability of the proposed wavelet method.

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“…is the .i, j/th component of the n C 1 by n C 1 matrix D, which is called the differentiation matrix [32]. According to (8), the entries of differentiation matrix D are computed by taking the analytical derivative of ' i .t/ and evaluating it in collocation points j for i, j D 0, : : : , n. However, more computationally practical methods for deriving these entries, in an accurate and stable manner, can be found in [33]. It is noted that the round-off error of the kth derivative is almost of order O. n 2k / [34,35], where is the machine precision and n is the number of discretization points.…”

Section: The Proposed Pseudospectral Methodsmentioning

confidence: 99%

An efficient pseudospectral method for numerical solution of nonlinear singular initial and boundary value problems arising in astrophysics

Mehrpouya

2015

Math Methods in App Sciences

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In the manuscript, a pseudospectral method is developed for approximate and efficient solution of nonlinear singular Lane-Emden-Fowler initial and boundary value problems arising in astrophysics. In the proposed method, the Gauss pseudospectral method is utilized to reduce the problem to the solution of a system of algebraic equations. Furthermore, the Gauss pseudospectral method is developed for finding the first zero of the solution of this equation that gives the radius of the star, in which the numerous properties of the star such as mass, central pressure, and binding energy can be computed through their relations to this solution. The main advantage of the proposed method is that good results are obtained even by using a small number of discretization points and the rate of convergence is high. The accuracy and performance of the proposed method are examined by means of some numerical experiments.

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An efficient numerical technique for the solution of nonlinear singular boundary value problems

Cited by 90 publications

References 39 publications

On the numerical solution of singular two‐point boundary value problems: A domain decomposition homotopy perturbation approach

On the numerical solution of singular two‐point boundary value problems: A domain decomposition homotopy perturbation approach

An efficient wavelet based spectral method to singular boundary value problems

An efficient pseudospectral method for numerical solution of nonlinear singular initial and boundary value problems arising in astrophysics

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