New approach on conventional solutions to nonlinear partial differential equations describing physical phenomena

Abstract

In current study, the modified variational iteration algorithm-I is investigated in the form of the analytical and numerical treatment of different types of nonlinear partial differential equations modelling physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection. In this modified algorithm, a supplementary parameter which guarantees a faster convergence rate is presented. Appropriate values of the additional parameter are obtained after minimization of properly defined error functions. The obtained results are compared against the exact solutions as well as against numerical solutions generated by the compact finite-difference method, fourth-order finite difference scheme, the second kind Chebyshev wavelets, DQ Chebyshev, and DQ Lagrange methods to show the efficiency, precision and implementation of the method. The proposed algorithm is considered as a very good technique for solving practical problems resulting in different fields of applied physical sciences and engineering.

Keywords

• Modified variational iteration algorithm-I
• Physical phenomena
• Diffusion equation
• Convection–diffusion equation