A new extended B-spline approximation technique for second order singular boundary value problems arising in physiology

In this study, we have proposed an efficient numerical algorithm based on third degree modified extended B-spline (EBS) functions for solving time-fractional diffusion wave equation with reaction and damping terms. The Caputo time-fractional derivative has been approximated by means of usual finite difference scheme and the modified EBS functions are used for spatial discretization. The stability analysis and derivation of theoretical convergence validates the authenticity and effectiveness of the proposed algorithm. The numerical experiments show that the computational outcomes are in line with the theoretical expectations. Moreover, the numerical results are proved to be better than other methods on the topic.

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“…where α n i (t) are time dependent constants, to be determined, and the ECBS blending functions of degree 4, η i (z), are defined as [32,36]…”

Section: Modified Extended Cubic B-spline Functionsmentioning

confidence: 99%

A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms

et al. 2019

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“…Here λ, with −n(n − 2) ≤ λ ≤ 1, is a real number responsible for fine-tuning the curve, and n gives the degree of the ECBS used to generate different forms of ECBS functions. The approximate solution (V * ) r m = V * (x m , t r ) and its first two derivatives with respect to the spatial variable x at the rth time step can be expressed in terms of ξ m as [48]…”

Section: Extended Cubic B-spline Functionsmentioning

confidence: 99%

Numerical Treatment of Time-Fractional Klein–Gordon Equation Using Redefined Extended Cubic B-Spline Functions

et al. 2020

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In this article we develop a numerical algorithm based on redefined extended cubic B-spline functions to explore the approximate solution of the time-fractional Klein-Gordon equation. The proposed technique employs the finite difference formulation to discretize the Caputo fractional time derivative of order α ∈ (1, 2] and uses redefined extended cubic B-spline functions to interpolate the solution curve over a spatial grid. A stability analysis of the scheme is conducted, which confirms that the errors do not amplify during execution of the numerical procedure. The derivation of a uniform convergence result reveals that the scheme is O(h 2 + t 2−α) accurate. Some computational experiments are carried out to verify the theoretical results. Numerical simulations comparing the proposed method with existing techniques demonstrate that our scheme yields superior outcomes.

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“…A hybrid form of cubic B-spline collocation method was applied to solve the different types of differential equations such as third-order Emden-Flower type equations [17], non-linear singular boundary value problems [18], third-order Korteweg-de Vries equation [1], second-order singular boundary value problems [34], etc. In the present work, an improvised collocation method is used to solve the gBH equation.…”

Section: Introductionmentioning

confidence: 99%

An improvised collocation algorithm to solve generalized Burgers’–Huxley equation

Shallu

Kukreja

2022

Arab. J. Math.

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In the proposed work, an improvised collocation technique with cubic B-spline as basis functions is applied to obtain the numerical solution of non-linear generalized Burgers’–Huxley equation, which has application in the soliton theory. In this technique, posteriori corrections are made to the cubic B-spline interpolant and its higher-order derivatives, which leads to enhancement in the order of convergence in the spatial domain. The temporal domain is discretized using a weighted finite difference scheme, to obtain the solution at each time level and the spatial domain is discretized using the improvised cubic B-spline collocation method. The stability analysis is carried out using the von Neumann scheme and the technique is found to be unconditionally stable. The theoretical proof of the order of convergence is discussed in detail using Green’s function approach. The $$L_{2}$$ L 2 , $$L_{\infty }$$ L ∞ , and absolute error norms are calculated as well as compared with the results available in the literature, which shows the improvement and efficacy of the proposed technique over the existing ones.

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A new extended B-spline approximation technique for second order singular boundary value problems arising in physiology

Cited by 15 publications

References 29 publications

A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms

A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms

Numerical Treatment of Time-Fractional Klein–Gordon Equation Using Redefined Extended Cubic B-Spline Functions

An improvised collocation algorithm to solve generalized Burgers’–Huxley equation

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