A new approach to the nonlinear advection problem: An application of the decomposition method
The author uses the decomposition method of Adomian for solving the nonlinear parabolic (advection) equation \[ {\partial u \over \partial t} + u {\partial u \over \partial x} = f(x,t) \quad \text{with initial condition} \quad u(x,0) = g(x). \] The solution is obtained as a (truncated) series by calculating Adomian polynomials. Reviewer's remark: The author does not know recent works by K. Abbaoui and Y. Cherruault for estimating the accuracy of the method and for calculating easily (formal calculus) Adomian polynomials associated to any nonlinear operator.
nonlinear parabolic (advection) equation
scientific article; zbMATH DE number 839108