New cubic B-spline approximation for solving third order Emden–Flower type equations

Iqbal, Muhammad Kashif; Abbas, Muhammad; Wasim, Imtiaz

doi:10.1016/j.amc.2018.03.025

Cited by 49 publications

(40 citation statements)

References 27 publications

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“…To show the versatility of numerical algorithm, we have presented four numerical experiments. The accuracy and efficiency of the method is tested by the maximum, Euclidian and the global relative error (GRE) norms, which are calculated as [27,42]…”

Section: Numerical Resultsmentioning

confidence: 99%

Application of new quintic polynomial B-spline approximation for numerical investigation of Kuramoto–Sivashinsky equation

et al. 2020

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A spline is a piecewise defined special function that is usually comprised of polynomials of a certain degree. These polynomials are supposed to generate a smooth curve by connecting at given data points. In this work, an application of fifth degree basis spline functions is presented for a numerical investigation of the Kuramoto–Sivashinsky equation. The finite forward difference formula is used for temporal integration, whereas the basis splines, together with a new approximation for fourth order spatial derivative, are brought into play for discretization in space direction. In order to corroborate the presented numerical algorithm, some test problems are considered and the computational results are compared with existing methods.

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Section: Numerical Resultsmentioning

confidence: 99%

Application of new quintic polynomial B-spline approximation for numerical investigation of Kuramoto–Sivashinsky equation

et al. 2020

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“…The accuracy of the current scheme is verified by the error norms L ∞ , L 2 and experimental order of convergence (EOC) [22,23]:…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

A fourth order non-polynomial quintic spline collocation technique for solving time fractional superdiffusion equations

et al. 2019

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The purpose of this article is to present a technique for the numerical solution of Caputo time fractional superdiffusion equation. The central difference approximation is used to discretize the time derivative, while non-polynomial quintic spline is employed as an interpolating function in the spatial direction. The proposed method is shown to be unconditionally stable and O(h 4 + t 2 ) accurate. In order to check the feasibility of the proposed technique, some test examples have been considered and the simulation results are compared with those available in the existing literature.

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“…where D j (t n+1 )s are unknowns to be identified and B j (z) are third degree basis spline functions defined as follows [27]:…”

Section: Description Of Numerical Methodsmentioning

confidence: 99%

Solving time fractional Burgers’ and Fisher’s equations using cubic B-spline approximation method

et al. 2020

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This article presents a numerical algorithm for solving time fractional Burgers' and Fisher's equations using cubic B-spline finite element method. The L1 formula with Caputo derivative is used to discretized the time fractional derivative, whereas the Crank-Nicolson scheme based on cubic B-spline functions is used to interpolate the solution curve along the spatial grid. The numerical scheme has been implemented on three test problems. The obtained results indicate that the proposed method is a good option for solving nonlinear fractional Burgers' and Fisher's equations. The error norms L 2 and L ∞ have been calculated to validate the efficiency and accuracy of the presented algorithm.

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New cubic B-spline approximation for solving third order Emden–Flower type equations

Cited by 49 publications

References 27 publications

Application of new quintic polynomial B-spline approximation for numerical investigation of Kuramoto–Sivashinsky equation

Application of new quintic polynomial B-spline approximation for numerical investigation of Kuramoto–Sivashinsky equation

A fourth order non-polynomial quintic spline collocation technique for solving time fractional superdiffusion equations

Solving time fractional Burgers’ and Fisher’s equations using cubic B-spline approximation method

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