ABSTRACT
The goal of this research work is to solve some nonlinear CDR (Convection-
Diffusion-Reaction) problems using VI (Variation Iteration). MVI (Modified
Variational Iteration) and coupling of VI with the modern wavelets methods.
Furthermore, combining the modern wavelet functions like LW (Legendre Wavelet)
and CW (Chebyshev Wavelet) with VIM an algorithm is derived for the solution of
nonlinear CDR PDE (Partial Differential Equations). The CDR PDE contains two
nonlinear terms called the reaction and convection terms. These methods fall in the
class of approximate methods using the initial solutions depending on the given
space. These a priori defended functions are generally considered as initial
conditions for the given nonlinear problems. The designed iterative procedure is
based on the idea of variational iteration methods along with LMT (Lagrange
Multiplier Technique). This method is applied to achieve the fast convergence from
the successive approximations of the exact solution without any restricting
approximations that may change the physical condition of the nonlinear problem.
The effects on the solution are also highlighted by selection of the various parameters
like, diffusion parameter, convection parameter and reaction parameter.
The approximating behavior, the efficiency, the accuracy analysis and the
simulations for the obtained solution are the heart of this research work. The
satiability of the designed numerical algorithm will be observed on the choice of
various time steps, moreover the overall performance of the algorithm will be
analyzed by comparing the results with well rated existing numerical schemes for
this particular class of problems.