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

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  • Iqbal, Muhammad Kashif
  • Abbas, Muhammad
  • Wasim, Imtiaz

Abstract

In this article, the typical cubic B-spline collocation method equipped with new approximations for second and third order derivatives is employed to explore the numerical solution of a class of third order non-linear singular boundary value problems. The singularity is removed by means of L’Hospital’s Rule. The Taylor’s series expansion of the error term reveals that our new scheme is fifth order accurate. The proposed technique is tested on several third order Emden–Flower type equations and the numerical results are compared with those found in the current literature. It is found that our new approximation technique performs superior to the existing methods due to its simple implementation, straight forward interpolation and very less computational cost.

Suggested Citation

  • Iqbal, Muhammad Kashif & Abbas, Muhammad & Wasim, Imtiaz, 2018. "New cubic B-spline approximation for solving third order Emden–Flower type equations," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 319-333.
    • Handle: RePEc:eee:apmaco:v:331:y:2018:i:c:p:319-333
    DOI: 10.1016/j.amc.2018.03.025
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    Cited by:

    1. Zafar, Zain Ul Abadin & Younas, Samina & Hussain, Muhammad Tanveer & Tunç, Cemil, 2021. "Fractional aspects of coupled mass-spring system," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Aydinlik, Soner & Kiris, Ahmet & Roul, Pradip, 2022. "An effective approach based on Smooth Composite Chebyshev Finite Difference Method and its applications to Bratu-type and higher order Lane–Emden problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 193-205.
    3. Kumar, Ajay & Kumar, Sunil, 2022. "A study on eco-epidemiological model with fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    4. Busyra Latif & Samsul Ariffin Abdul Karim & Ishak Hashim, 2021. "New Cubic B-Spline Approximation for Solving Linear Two-Point Boundary-Value Problems," Mathematics, MDPI, vol. 9(11), pages 1-13, May.
    5. Ishtiaq Ali & Muhammad Yaseen & Muhammad Abdullah & Sana Khan & Fethi Bin Muhammad Belgacem, 2023. "An Innovative Numerical Method Utilizing Novel Cubic B-Spline Approximations to Solve Burgers’ Equation," Mathematics, MDPI, vol. 11(19), pages 1-19, September.

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