article · BIMA JOURNAL OF SCIENCE AND TECHNOLOGY GOMBE
This research developed and compared two numerical methods, the Homotopy Perturbation Method (HPM) and the Series Solution Method (SSM), for solving linear Volterra integral equations. These equations are often challenging to solve analytically. The HPM approach involved constructing a homotopy and using a perturbation expansion in terms of power series. The SSM assumed a power series solution, substituting it into the problem and comparing coefficients to find unknown constants. Numerical examples were used to demonstrate the simplicity, reliability, and efficiency of both methods. The findings indicate that these methods are accurate and perform better than other existing techniques.
Integral equations are fundamental in many scientific and engineering fields, but often lack analytical solutions. Developing more accurate and reliable numerical methods is crucial for effectively modelling complex systems and making precise predictions in areas like physics, engineering, and finance.
The abstract indicates that these methods are more accurate and reliable than existing ones for solving linear Volterra integral equations. This suggests potential for integration into specialised computational software or simulation platforms used by engineers, physicists, and data scientists. This is early-stage research focused on improving foundational numerical techniques for broader application.
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The aim of this research paper is to develop numerical methods of solving linear Volterra integral equations using Homotopy Perturbation Method (HPM) and Series Solution Method (SSM). Most Integral equations are difficult to solve analytically, hence the need for a more accurate and reliably numerical method. In the the Homotopy Perturbation approach, the modelled problem is used to construct a homotopy and a perturbation expansion in terms of power series was assumed while in the series solution method, a power series solution was assumed and the assumed solution was substituted into the modelled problem by comparing the coefficient of like terms to obtain the unknown constants. The results of the two methods were compared and numerical examples were used to establish the simplicity, reliability and efficiency of the methods. The result shows that the methods are accurate and outperforms other methods existing in literature.
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DOI: 10.64290/bima.v9i1a.893
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