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An effective approach based on Smooth Composite Chebyshev Finite Difference Method and its applications to Bratu-type and higher order Lane–Emden problems

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  • Aydinlik, Soner
  • Kiris, Ahmet
  • Roul, Pradip

Abstract

The Smooth Composite Chebyshev Finite Difference method is generalized for higher order initial and boundary value problems. Round-off and truncation error analyses and convergence analysis of the method are also extended to higher order. The proposed method is applied to obtain the highly precise numerical solutions of boundary or initial value problems of the Bratu and higher order Lane Emden types. To visualize the competency of the presented method, the obtained results are compared with nine different methods, namely, Bezier curve method, Adomian decomposition method, Operational matrix collocation method, Direct collocation method, Haar Wavelet Collocation, Bernstein Collocation Method, Improved decomposition method, Quartic B-Spline method and New Cubic B-spline method. The comparisons show that the presented method is highly accurate than the other numerical methods and also gets rid of the singularity of the given problems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:202:y:2022:i:c:p:193-205
    DOI: 10.1016/j.matcom.2022.05.032
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    References listed on IDEAS

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    1. Ramos, J.I., 2008. "Series approach to the Lane–Emden equation and comparison with the homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 400-408.
    2. A. Kazemi Nasab & A. Kılıçman & Z. Pashazadeh Atabakan & S. Abbasbandy, 2013. "Chebyshev Wavelet Finite Difference Method: A New Approach for Solving Initial and Boundary Value Problems of Fractional Order," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-15, December.
    3. 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.
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