Solutions of Volterra Integral Equations (VIEs) of the Second Kind with Bulge Function using Aboodh Transform - Asif Iqbal Ali; Muhammad Kalim; Adnan Khan (Scientific Inquiry and Review, 2022)
A large class of complexities in mathematical physics, applied mathematics, and engineering are expressed as differential equations with few additions and certain conditions. This research focuses on the solution of Volterra integral equations (VIEs) of the second kind, with bulge functions as known functions. To obtain an analytical solution, the Aboodh transform, the Aboodh inverse transform, and the convolution theorem are employed, since it is required to discover the precise solution of VIEs. This solution is compared with a numerical solution using the modified Simpson method. Finally, it is represented graphically.