Daftardar-Jafari Method for Solving the Damped Generalized Regularized Long-Wave Equation

In this work, the Daftardar-Jafari method has been submitted to deal with the approximated solutions for the nonlinear damped generalized regularized long-wave (DGRLW) equation with some given variable coefficient. by using this iterative technique we have got rid of any additional assumptions in order to get the solution of the nonlinear DGRLW equation where this solution has been evaluated in a series form with several computable components. Three numerical examples have been tested to show the easy-applicable scheme for the method where the third example has been solved by using the modified Daftardar-Jafari method in order to deal with an inhomogeneous case for the DGRLW equation. Also, our approximate solutions have been numerically reported and figured with the exact solution.