The decomposition method for approximate solution of the Goursat problem
Applied Mathematics and Computation
Necessary conditions for the appearance of noise terms in decomposition solutions series
Applied Mathematics and Computation
Nonlinear partial differential equations: for scientists and engineers
Nonlinear partial differential equations: for scientists and engineers
Explicit solutions of nonlinear partial differential equations
Applied Mathematics and Computation
A reliable technique for solving the wave equation in an infinite one-dimensional medium
Applied Mathematics and Computation
A comparison between Adomian decomposition method and Taylor series method in the series solutions
Applied Mathematics and Computation
Analytical approximations and Padé approximants for Volterra's population model
Applied Mathematics and Computation
A computational algebraic investigation of the decomposition method for time-dependent problems
Applied Mathematics and Computation
Solution of nonlinear equations by modified adomian decomposition method
Applied Mathematics and Computation
Mathematics and Computers in Simulation
The decomposition method for forward and backward time-dependent problems
Journal of Computational and Applied Mathematics
Convergence of Adomian's method applied to nonlinear equations
Mathematical and Computer Modelling: An International Journal
New results for convergence of Adomian's method applied to integral equations
Mathematical and Computer Modelling: An International Journal
Decomposition methods: A new proof of convergence
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
Random volterra integral equations
Mathematical and Computer Modelling: An International Journal
Practical formulae for the calculus of multivariable adomian polynomials
Mathematical and Computer Modelling: An International Journal
Journal of Computational and Applied Mathematics
Dynamics and synchronization of numerical solutions of the Burgers equation
Journal of Computational and Applied Mathematics
ADM-Padé solutions for generalized Burgers and Burgers-Huxley systems with two coupled equations
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
The application of Adomian's decomposition method to partial differential equations, when the exact solution is not reached, demands the use of truncated series. But the solution's series may have small convergence radius and the truncated series may be inaccurate in many regions. In order to enlarge the convergence domain of the truncated series, Pade approximants (PAs) to the Adomian's series solution have been tested and applied to partial and ordinary differential equations, with good results. In this paper, PAs, both in x and t directions, applied to the truncated series solution given by Adomian's decomposition technique for Burgers equation, are tested. Numerical and graphical illustrations show that this technique can improve the accuracy and enlarge the domain of convergence of the solution. It is also shown in this paper, that the application of Adomian's method to the ordinary differential equations set arising from the discretization of the spatial derivatives by finite differences, the so-called method of lines, may reduce the convergence domain of the solution's series.