(untitled) (Journal of Partial Differential Equations, 2020)
New developed inverse differential operators incorporated into the semianalytical treatment of the modified decomposition method (MDM) are used to solve the systems of first and second-order singular nonlinear partial differential equations (PDEs) with initial conditions arising in physics. The new proposed method is called the improved modified decomposition method (IMDM), and is used to the treatment of a few case study initial-value problems. The results obtained by the IMDM are in full agreement with the existing exact analytical solutions.