Investigation in the neighborhood of a moving singular point of a certain class of a third-order nonlinear differential equation for a complex domain
In this paper, we study a certain class of differential equations with moving singularities. A generalization of the previously obtained results of the study, namely, the existence and uniqueness theorem for the solution of the considered class of equations, to the complex domain is given. The structure of the analytical approximate solution and a priori error estimates are obtained. These estimates were optimized using post hoc estimates. Theoretical provisions were tested using a numerical experiment.