A sixth-order numerical method for a strongly nonlinear singular boundary value problem governing electrohydrodynamic flow in a circular cylindrical conduit

Roul, Pradip; Madduri, Harshita; Kassner, Klaus

doi:10.1016/j.amc.2018.12.070

Cited by 12 publications

(15 citation statements)

References 36 publications

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“…In the study of EHD flow, we observed that the effects of Hartmann number and nonlinearity have an important impact. Further we also compare our results with the results of SSNM [29], Haar [35], ADM [36], and OHAM [34]. The graphs show the efficiency of our methods.…”

Section: Resultsmentioning

confidence: 74%

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On some wavelet solutions of singular differential equations arising in the modeling of chemical and biochemical phenomena

2020

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This paper is concerned with the Lane–Emden boundary value problems arising in many real-life problems. Here, we discuss two numerical schemes based on Jacobi and Bernoulli wavelets for the solution of the governing equation of electrohydrodynamic flow in a circular cylindrical conduit, nonlinear heat conduction model in the human head, and non-isothermal reaction–diffusion model equations in a spherical catalyst and a spherical biocatalyst. These methods convert each problem into a system of nonlinear algebraic equations, and on solving them by Newton’s method, we get the approximate analytical solution. We also provide the error bounds of our schemes. Furthermore, we also compare our results with the results in the literature. Numerical experiments show the accuracy and reliability of the proposed methods.

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Section: Resultsmentioning

confidence: 74%

“…The numerical solution of (1.6) for σ = 0.5, 1, 1.5 is given in Table 6. We compare our results with the results of OHAM [29] in Table 7.…”

Section: Numerical Treatment Of Spherical Catalyst Equationmentioning

confidence: 93%

On some wavelet solutions of singular differential equations arising in the modeling of chemical and biochemical phenomena

2020

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“…Equations (30), (32) and (33) yield a system of M + 3 equations in M + 5 unknowns. In order to obtain a unique solution to this system we need two extra auxiliary equations.…”

Section: Spatial Discretizationmentioning

confidence: 99%

“…Using (32) and (33), the unknowns n −2 , n M+2 ,̂n −2 and̂n M+2 have been eliminated from the first two rows and last two rows of the above system. Thus, we obtain…”

Section: Theoremmentioning

confidence: 99%

“…The proposed method is fourth order convergence in space and (2 − )-th order convergence in time. Various numerical schemes based on B-spline collocation methods have been applied to solve a wide variety of problems, see [24][25][26][27][28][29][30][31][32][33][34]. Besides B-spline collocation techniques, there are other methods that can be used to solve classic or fractional differential equations, such as finite difference methods [6,7,14], finite element method [35], boundary element methods [36,37], meshless methods [38,39] etc.…”

Section: Introductionmentioning

confidence: 99%

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A high order numerical scheme for solving a class of non‐homogeneous time‐fractional reaction diffusion equation

Roul

Goura

2020

Numerical Methods Partial

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This paper is concerned with the development of a high order numerical technique for solving time‐fractional reaction–diffusion equation. The fractional derivative in the governing equation is described in the Caputo sense and a collocation method based on quintic B‐spline basis function is used to discretize the space variable. The stability and convergence analysis of the method are investigated, and it is shown that the proposed method converges to the exact solution of the problem with order of convergence O(Δt2 − α + Δx4), where α is the order of fractional derivative (0 < α < 1). Three test problems are considered to illustrate the efficiency and accuracy of present numerical scheme and to verify the theoretical result. It is shown that the order of fractional derivative has a profound effect on the solution of time‐fractional reaction–diffusion equation.

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A high‐order efficient technique and its convergence analysis for Bratu‐type and Lane‐Emden‐type problems

Roul

Goura

2022

Math Methods in App Sciences

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The present work deals with the construction of a high‐order efficient technique for solving one‐dimensional nonlinear Bratu‐type and Lane‐Emden‐type problems describing various physical, chemical and biological phenomena in applied science and engineering. Convergence analysis of the method is studied. Numerical experiments are carried out to demonstrate the efficiency, accuracy and performance of proposed method. The method is shown to have sixth order convergence. The computed results are compared with those obtained by other numerical techniques to justify the advantage of present scheme. It is shown that the proposed method is fast convergent and provides accurate solutions for Bratu‐type and Lane‐Emden‐type problems with low computational cost.

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A sixth-order numerical method for a strongly nonlinear singular boundary value problem governing electrohydrodynamic flow in a circular cylindrical conduit

Cited by 12 publications

References 36 publications

On some wavelet solutions of singular differential equations arising in the modeling of chemical and biochemical phenomena

On some wavelet solutions of singular differential equations arising in the modeling of chemical and biochemical phenomena

A high order numerical scheme for solving a class of non‐homogeneous time‐fractional reaction diffusion equation

A high‐order efficient technique and its convergence analysis for Bratu‐type and Lane‐Emden‐type problems

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