Residual Power Series Method for Solving Linear Complex Differential Equations

Abstract

This work uses the residual power series method (RPSM), primarily based on the general Taylor series formula with a residual error function, to offer solutions to instances of linear complex differential equations (LCDEs) as test problems. After finding approximate solutions to those problems, the current approach's findings have been compared with the exact solutions as shown in the tables and figures, which show the suggested method's reliability, precision, and rapid convergence. So, the importance of this research lies in demonstrating the method's ability to find an approximate solution close to the exact solution for complex differential equations.