Solutions of partial differential equations are of great importance for mathematicians and scientists. In this paper, the author likewise calculated exact Langrage multiplier and it progressively connects to the definite results of Helmholtz and nonlinear parabolic equations. This study shows the advantages of exact Lagrange multipliers and their coupling with Variational Iteration Method. Computational work shows that the use of exact Lagrange multipliers reduces the computational work to a tangible level and also increases the level of accuracy. Moreover, exact Lagrange multiplier reduces the successive application of integral operator and is more user friendly.

Keywords: Exact Langrage multiplier (ELM), approximate Langrage multiplier (ALM), variational iteration method (VIM), decomposition method (ADM & MADM), Helmholtz Equations, non-linear parabolic equation.