Numerical Doubly-Periodic Solutions of (2+1)-Dimensional Boussinesq Equation Via an Improved Decomposition Scheme

In this paper, an improved scheme is presented to investigate the approximate solutions of (2+1)-dimensional Boussinesq equation with initial conditions based on the decomposition method. The improve scheme makes all components ui of u = ∑∞ i=0 ui be of the same degree in t. We choose the (2+1)-dimensional Boussinesq equation with initial conditions of doubly-periodic functions to illustrate the scheme. As a result, the approximate and exact doubly-periodic solutions are obtained. For differential modulus m = 0.1, 0.9, we compare the approximate solution with the exact solution by their graphs. Moreover we analyze the absolute error and relative error, and give the contour and density plots of the approximate doubly-periodic solutions.