Exploring Solution Strategies for Volterra Integro-Differential Lane–Emden Equations in Astrophysics Using Haar Scale 3 Wavelets
The current research introduces a novel approach to address the computational challenges associated with solving the Lane–Emden-type equations by transforming them from their conventional differential form to the corresponding integro-differential form. These equations have wide-ranging applications...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2024/5561911 |
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| Summary: | The current research introduces a novel approach to address the computational challenges associated with solving the Lane–Emden-type equations by transforming them from their conventional differential form to the corresponding integro-differential form. These equations have wide-ranging applications in physical sciences, including modeling diffusion phenomena and thermal gradients. We utilize the Volterra integro-differential (VID) form to resolve computational challenges due to singularity issues. Through the Scale 3 Haar Wavelet (S3-HW) algorithm, we transform the VID equations into algebraic form and obtain solutions using the Gauss-elimination method. The quasilinearization technique is implemented whenever a nonlinearity is encountered. Comparative analysis against various techniques demonstrates the superior accuracy and efficiency of our method. Despite challenges such as the discontinuity of Scale 3 Haar Wavelets and singularity issues of Lane–Emden-type equations, our algorithm paves the way for extending its application to a wide range of physical problems. |
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| ISSN: | 1687-9139 |