The numerical approximation of discrete Vlasov–Darwin model based on the optimal reformulation of field equations

In this article we discuss the elliptic reformulation of initial-boundary problem for Vlasov–Maxwell equation system in general three-dimensional (3D3V) case. We briefly describe a scheme of its numerical solution with the PIC method, that allows building correct nonradiative algorithms. Achieved redaction of original initial-boundary problem is easily adaptable both to fractional-dimensional (2D3V) formulations and to different sets of boundary conditions.