Ikechukwu Jackson Otaide

In this paper, the Elzaki transform series decomposition method is used numerically to solve nonlinear Bratu differential equations. The method combines the Elzaki transform, series expansion and Adomian polynomials, and hence converges absolutely to the exact solution. Additionally, two numerical examples were presented to illustrate the efficacy and dependability of the suggested approach. Applications for the work can be found in mathematics as well as a number of other scientific and engineering disciplines. Calculations were done using maple 2018 software.

This study presents a numerical solution of the Bratu differential equations (BDE) using the Sumudu transform series decomposition technique (STSDT). The process combines the Adomian polynomials (AP), series expansion (SE), and Sumudu transform (ST), and it ultimately converges perfectly to the exact solution. Examining four test problems demonstrates that the strategy converges more effectively than the literature-based approach. Calculations were performed using Maple 2022 software.

In this study, the numerical solution of the Volterra-integro differential equations was obtained by applying the variational iteration strategy with the shifted Vieta-Lucas polynomials. The proposed method builds the shifted Vieta-Lucas polynomials for the Volterra-integro differential equation which are then used as basis functions for the approximation. Numerical examples were given to establish the effectiveness and dependability of the recommended approach. Calculations were performed using Maple 2022 software.