AN EFFECTIVE NUMERICAL ALGORITHM FOR SOLVING THE LANE-EMDEN TYPE EQUATION BASED ON THE VARIATIONAL ITERATION METHOD COUPLED WITH THE HOMOTOPY ANALYSIS METHOD

Vikash Kumar Sinha; Prashanth Maroju

doi:10.11948/20240255

2025 Volume 15 Issue 2

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Vikash Kumar Sinha, Prashanth Maroju. AN EFFECTIVE NUMERICAL ALGORITHM FOR SOLVING THE LANE-EMDEN TYPE EQUATION BASED ON THE VARIATIONAL ITERATION METHOD COUPLED WITH THE HOMOTOPY ANALYSIS METHOD[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 1091-1106. doi: 10.11948/20240255

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Vikash Kumar Sinha, Prashanth Maroju. AN EFFECTIVE NUMERICAL ALGORITHM FOR SOLVING THE LANE-EMDEN TYPE EQUATION BASED ON THE VARIATIONAL ITERATION METHOD COUPLED WITH THE HOMOTOPY ANALYSIS METHOD[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 1091-1106. doi: 10.11948/20240255

AN EFFECTIVE NUMERICAL ALGORITHM FOR SOLVING THE LANE-EMDEN TYPE EQUATION BASED ON THE VARIATIONAL ITERATION METHOD COUPLED WITH THE HOMOTOPY ANALYSIS METHOD

Vikash Kumar Sinha^1,,
Prashanth Maroju^1, ,

1.
Department of Mathematics, SAS, VIT-AP University, 522237 Amaravati, Andhra Pradesh, India

Author Bio: Email: sinha.vikash2420@gmail.com(V. K. Sinha)
Corresponding author: Email: maroju.prashanth@gmail.com(P. Maroju)

Abstract

Abstract

This research introduces an effective numerical algorithm to determine the numerical solution of the Lane-Emden equation. This method is based on the variational iteration method coupled with the homotopy analysis method. We also included the convergence study of the proposed algorithm. Eight application problems of the Lane-Emden type equation of various kinds with several types of initial and boundary conditions are included to demonstrate the efficacy and accuracy of the proposed algorithm. The numerical outcomes are contrasted with those obtained by other methods [12,20,21] and the exact solution. Unlike other methods, the proposed algorithm does not require discretization or perturbation and can be applied easily and accurately. The proposed method can solve complex problems with less computational work and computation time.
- Astrophysics /
- Lane-Emden equation /
- homotopy analysis method /
- variational iteration method
MSC: 65Lxx, 65L05

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References

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