Solving Volterra Integral Equations with Difference Kernel Using Laplace Transforms
DOI:
https://doi.org/10.37375/foej.v5i1.3808Keywords:
Analytical Solution, Difference Kernel, Integral Equations, Laplace Transform, Volterra EquationAbstract
Integral equations are a fundamental mathematical tool for modeling many phenomena in physics, engineering, and biology. This study focuses on the application of the Laplace transform as an effective analytical method for solving linear Volterra integral equations of the second kind, specifically those where the kernel is a function of the difference. The strength of this technique lies in its ability to transform the integral equation into an algebraic equation in the Laplace domain, significantly simplifying the process of finding an explicit solution. The paper presents the theoretical framework of the Laplace transform and its key properties, followed by a classification of integral equations. The method is then demonstrated through practical, solved examples, proving its efficiency and accuracy in obtaining solutions. The results expected to confirm that the Laplace transform method is a powerful and reliable analytical tool for this important class of integral equations.
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