In this paper, we present a numerical method for solving nonlinear differential algebraic equations (DAE’s) based on the backward differential formulas (BDF) and the Pade series. Usefulness of the method is then illustrated by a numerical example, which is concerned with the derivation of the optimal guidance law for spacecraft. This kind of problems is called trajectory-prescribed path control...

Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these variational characterizations instead of the partial differential equations themselves, we obtain new schemes with remarkable stability properties. We show that they c...

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This work aims at the exploration of production data analysis (PDA) methods without iterations. It can overcome limitations advanced type curve relying on iterative calculation material-balance pseudotime and current explicit reckoning specific schedule assumptions. The dynamic material balance equation (DMBE) is strictly proved by integral variable substitution based gas flow under boundary do...

Wheel-rail systems can be modelled as mechanical multibody systems with holonomic constraints. The dynamical behaviour is described by a diierential-algebraic system of index 3 in non{Hessenberg form ((10]). We discuss the eecient numerical solution of these model equations. A perturbation analysis suggests the integration of the model equations in the Gear{Gupta{Leimkuhler (GGL) formulation. T...