Adomian decomposition method for the one-dimensional nonlocal Fisher - Kolmogorov - Petrovskii - Piskunov equation
The Adomian decomposition method is applied to construct an approximate solution of the generalized one-dimensional Fisher - Kolmogorov - Petrovsky - Piskunov equation describing population dynamics with nonlocal competitive losses. An approximate solution is constructed in the class of decreasing functions. The diffusion operator is taken as a reversible linear operator. The inverse operator is presented in terms of the diffusion propagator. An example of an approximate solution of the Cauchy problem for the function of competitive losses and the initial function of the Gaussian form is considered.