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Collocation Technique Based on Chebyshev Polynomials to Solve Emden–Fowler-Type Singular Boundary Value Problems with Derivative Dependence

Author

Listed:
  • Shabanam Kumari

    (Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India)

  • Arvind Kumar Singh

    (Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India)

  • Utsav Gupta

    (Tanglin Trust School, 95 Portsdown Rd, Singapore 139299, Singapore)

Abstract

In this work, an innovative technique is presented to solve Emden–Fowler-type singular boundary value problems (SBVPs) with derivative dependence. These types of problems have significant applications in applied mathematics and astrophysics. Initially, the differential equation is transformed into a Fredholm integral equation, which is then converted into a system of nonlinear equations using the collocation technique based on Chebyshev polynomials. Subsequently, an iterative numerical approach, such as Newton’s method, is employed on the system of nonlinear equations to obtain an approximate solution. Error analysis is included to assess the accuracy of the obtained solutions and provide insights into the reliability of the numerical results. Furthermore, we graphically compare the residual errors of the current method to the previously established method for various examples.

Suggested Citation

  • Shabanam Kumari & Arvind Kumar Singh & Utsav Gupta, 2024. "Collocation Technique Based on Chebyshev Polynomials to Solve Emden–Fowler-Type Singular Boundary Value Problems with Derivative Dependence," Mathematics, MDPI, vol. 12(4), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:592-:d:1340316
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    References listed on IDEAS

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    1. Roul, Pradip & Prasad Goura, V.M.K., 2019. "B-spline collocation methods and their convergence for a class of nonlinear derivative dependent singular boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 428-450.
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