The Iterative Bayawa Transform-Adomian Decomposition Method for Solving Various Classes of Linear and Nonlinear Integral Equations.
DOI:
https://doi.org/10.54172/ch8x9748Keywords:
Bayawa Transform, Adomian Decomposition Method, Volterra Inte-gral Equations, Fredholm Integro-Differential Equations, Volterra Integro-Differential Equations, Combined Bayawa Transform-Adomian Decomposition.Abstract
Integral transforms can be directly applied to solve various classes of Volterra integral equations, including those with convolutional kernels and linear Volterra integro-differential equations. However, solving nonlinear Volterra and Fredholm integro-differential equations requires decomposing the integral transform with one of the established methods for solving integral equations, such as the Adomian Decomposition Method. In this paper, we demonstrate how the Bayawa integral transform, either independently or in combination with the Adomian decomposition method, can be employed to solve various classes of integral equations, depending on their type. To verify the method’s efficiency, we solve diverse examples of integral equations, obtaining exact or approximate solutions based on their complexity. The obtained results show that the iterative Bayawa transform-Adomian decomposition approach effectively solves a wide range of IEs.
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