BACKWARD NORDSIECK’S METHODS FOR NUMERICAL SOLVING OF ORDINARY DIFFERENTIAL EQUATIONS

Abstract

where: z = (u, τu, τu, ... , τu ) – Nordsieck’s vector, τ – integration step, М – the number of terms in the Taylor series expansion of the function u(t), D, L – upper triangular and diagonal matrices whose element’s values di,j = { 1 (i−j)! , i ≥ j 0, i < j , li,i = τM−i+1 (M−i+1)! follow from the series expansion, q – a vector of free parameters that determines the properties of the numerical method,