APPLICATION OF ADOMIAN DECOMPOSITION METHODS IN SOLVING SOME SELECTED NON LINEAR PARTIAL DIFFERENTIAL EQUATIONS
Keywords:
nonlinear partial differential equation, Picard method, Burgers’ equation, Sine-Gordon equation, Advection equation, Adomian Decomposition MethodAbstract
This paper considers the nonlinear partial differential equations. The Adomian Decomposition Method (ADM) was proposed as a method for solving a special kind of nonlinear partial differential equation with attention focused on some selected nonlinear partial differential equation. The nonlinear partial differential equation considered in this study includes advection equation, Sine-Gordon equation and Burger’s equation, subject to given initial values. This method was subjected to test of convergence and it was observed that it converges rapidly. Adomian decomposition method was applied in solving the three nonlinear partial equations highlighted above and the method demonstrates that the solution is obtained with a fast convergence, thereby, making the method athematically
tractable and less approximation error. The effect of the noise term was reduced and this makes the method attractive and convenient. There is no need to transform the nonlinear term to linear terms before solving the adomian polynomial. Hence, the
method is effective and suitable for nonlinear partial differential equations with initial values.
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