In this work, the adomian decomposition method is proposed for the first time to solve problems in two-dimensional Volterra Integral equations of the second kind. In addition, modification of this method is introduced to address this problem. Several new theorems are introduced and proven regarding contractive mapping and uniform convergence to support the method. Numerical problems are solved using the software Matlab to obtain results and demonstrate the efficiency and simplicity of the technique. The modified Adomian decomposition method performs faster than the adomian decomposition method for obtaining results.
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Hassan et al. (2024) studied this question.
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