A third-order finite difference method on a quasi-variable mesh for nonlinear two point boundary value problems with Robin boundary conditions

Setia, Nikita; Mohanty, R. K.

doi:10.1007/s00500-021-06056-x

Cited by 5 publications

(3 citation statements)

References 37 publications

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“…Lu et al (2016) applied finite difference method via utilizing Padé approximation to deal with a numerical solution of the propagation of long waves on the surface of water. In addition, researchers developed compact finite difference schemes for solving singular nonlinear boundary value problems (Roul et al 2019, Setia and Mohanty 2021, Chawla et al 1986, Pandey and Singh 1978.…”

Section: Discretization Of the Equations Via Finite Difference Methodsmentioning

confidence: 99%

Rasyonel Üslü Cebirsel ve Üstel Eşleme Yaklaşımı ile Thomas-Fermi Denklemi için İkinci Derece Doğruluklu Sonlu Farklar Yöntemi

Karabulut

Koroglu

2023

Afyon Kocatepe University Journal of Sciences and Engineering

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Many problems based on natural sciences need to be solved by the scientists and engineers to serve the humanity. One of the well-known model in atomic universe is condensed into an equation, and called the Thomas-Fermi equation. It is a second order differential equation, which describes charge distributions of heavy, neutral atoms. No exact analytical solution has been found for the equation yet. In fact, strong nonlinearity, singular character and unbounded interval of the problem causes great difficulty to obtain an approximate numerical solution as well. In this paper, the Thomas-Fermi equation is solved using a second order finite difference method along with application of quasi-linearization method. Semi-infinite interval of the problem is converted into [0, 1) using two different coordinate transformations, namely algebraic and exponential mapping. Numerical order of accuracy has been checked using systematic mesh refinements and comparing the calculated initial slope y'(0). Calculated results for initial slope is found in good agreement with the results available in the literature. Lastly, accuracy is improved by the application of the Richardson extrapolation.

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Section: Discretization Of the Equations Via Finite Difference Methodsmentioning

confidence: 99%

Rasyonel Üslü Cebirsel ve Üstel Eşleme Yaklaşımı ile Thomas-Fermi Denklemi için İkinci Derece Doğruluklu Sonlu Farklar Yöntemi

Karabulut

Koroglu

2023

Afyon Kocatepe University Journal of Sciences and Engineering

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“…Our Scheme Scheme [15] Scheme [13] Our Scheme Scheme [15] Scheme [13] Fig. 5a: Example 5: Numerical and exact solution for q = 0.5 6 that the agreements between exact and numerical solutions are excellent.…”

mentioning

confidence: 89%

“…Compact FDM used by Roul et al [13] for nonlinear singular BVPs with mixed boundary conditions has proved to be very effective in solving various physical models. Moreover, FDM on quasi variable mesh has been developed for Robin boundary conditions by Mohanty and Talwar in [14] and [15] obtaining high order accuracy. Certain approaches mentioned above prove inadequate in performing computations on a finely graded mesh with derivative boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

A High-Resolution Exponential Spline Method and Its Convergence Analysis for Two-Point Mixed Boundary Value Problems

Sharma,

Kaur

2024

Int. J. Comput. Methods

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In this paper, we present a new numerical method for effectively solving general second-order ordinary differential equations with mixed boundary conditions. Our approach utilizes a quasi-variable mesh enabling us the flexibility to adapt the mesh density according to different boundary layer problems. By employing a discretization technique that incorporates the construction of exponential spline, we achieve third-order accuracy at internal grid points, while boundary points exhibit fourth-order accuracy. Since the method is based on off-step grid points, it eliminates the need to modify the method while employing it to singular problems. We provide computational results to various numerical problems which arise in different physical phenomena like Burger’s equation and Sturm–Liouville equation. A comparison with recent findings underscores the superior performance of our method.

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A high accuracy variable mesh numerical approximation for two point nonlinear BVPs with mixed boundary conditions

Setia

Mohanty²

2022

Soft Comput

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A third-order finite difference method on a quasi-variable mesh for nonlinear two point boundary value problems with Robin boundary conditions

Cited by 5 publications

References 37 publications

Rasyonel Üslü Cebirsel ve Üstel Eşleme Yaklaşımı ile Thomas-Fermi Denklemi için İkinci Derece Doğruluklu Sonlu Farklar Yöntemi

Rasyonel Üslü Cebirsel ve Üstel Eşleme Yaklaşımı ile Thomas-Fermi Denklemi için İkinci Derece Doğruluklu Sonlu Farklar Yöntemi

A High-Resolution Exponential Spline Method and Its Convergence Analysis for Two-Point Mixed Boundary Value Problems

A high accuracy variable mesh numerical approximation for two point nonlinear BVPs with mixed boundary conditions

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