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Updated: Jun 4, 2025
06:04
Simulation of the Planetary Interior Differentiation Processes in the Laboratory
Published on: November 15, 2013
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Unveiling protoplanetary structure equations: Semi-analytical solutions via the homotopy analysis method.
Gour Chandra Paul1, Tauhida2, Md Nuruzzaman3
1Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh.
Heliyon
|December 17, 2024
Summary
This study applies the Homotopy Analysis Method (HAM) to analyze thermodynamic variables in protoplanets formed by gravitational instability (GI). HAM shows rapid convergence and superior accuracy compared to other methods for these astrophysical models.
Area of Science:
- Astrophysics
- Planetary Science
- Computational Physics
Background:
- Gravitational instability (GI) is a key mechanism for protoplanet formation.
- Understanding thermodynamic distributions within protoplanets is crucial for planet formation theories.
- Traditional methods for solving nonlinear astrophysical problems can be computationally intensive.
Purpose of the Study:
- To investigate the distribution of thermodynamic variables in protoplanets formed via GI.
- To apply the Homotopy Analysis Method (HAM) as a novel approach for analyzing these systems.
- To compare the efficacy of HAM with existing numerical and analytical methods.
Main Methods:
- Utilized the Homotopy Analysis Method (HAM) for analyzing thermodynamic variables.
- Considered convective heat transfer within protoplanets.
- Compared HAM results (third approximation) with numerical outcomes and the Adomian decomposition method.
Main Results:
- HAM demonstrated rapid convergence towards exact solutions for nonlinear problems.
- Results from HAM (first four terms) showed strong agreement with numerical findings.
- HAM exhibited superior accuracy and analytical depth compared to the Adomian decomposition method.
Conclusions:
- The Homotopy Analysis Method (HAM) is an effective and accurate tool for studying astrophysical phenomena.
- HAM offers significant advantages over traditional methods for analyzing protoplanetary systems.
- This research validates HAM's potential for broader applications in astrophysical research.
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