Numerical Approximation of Some Nonlinear Partial Differential Equations by Laplace Decomposition Method

Amitha Manmohan Rao,Arundhati Suresh Warke

Laplace Decomposition Method(LDM) is implemented to obtain analytical and numerical solutions of some nonlinear partial differential equations(PDE’s) of Burger’s and Fisher’s type. As the convergence of the LDM highly depends upon the initial wave profile which is the combination of given initial condition and the source term, illustrative examples with flux functions of different nature and initial conditions are included to demonstrate the applicability of the method. The series solutions and absolute errors are calculated for different values of x and t to demonstrate high accuracy and rapid convergence of the LDM. Graphical representation in each case is given to understand the wave phenomena. MATLAB is used to compute Adomain polynomials and to plot graphs of the equations.

Volume 11 | 02-Special Issue

Pages: 2305-2311