  The purpose of the research is to find the numerical solutions to the system
of time dependent nonlinear parabolic partial differential equations (PDEs)
utilizing the Modified Galerkin Weighted Residual Method (MGWRM) with the help
of modified Bernstein polynomials. An approximate solution of the system has
been assumed in accordance with the modified Bernstein polynomials. Thereafter,
the modified Galerkin method has been applied to the system of nonlinear
parabolic PDEs and has transformed the model into a time dependent ordinary
differential equations system. Then the system has been converted into the
recurrence equations by employing backward difference approximation. However,
the iterative calculation is performed by using the Picard Iterative method. A
few renowned problems are then solved to test the applicability and efficiency
of our proposed scheme. The numerical solutions at different time levels are
then displayed numerically in tabular form and graphically by figures. The
comparative study is presented along with L2 norm, and L infinity norm.
