We analytically study the relationship between the Poincaré map and its one step discretization. Error estimates are established depending basically on the right hand side function of the investigated ODE and the given numerical scheme. Our basic tool is a parametric version of a Newton–Kantorovich type methods. As an application, in a neighborhood of a non-degenerate periodic solution a new ty...

This paper proposes an infeasible interior-point algorithm with full-Newton step for linear programming, which is an extension of the work of Roos (SIAM J. Optim., 16(4):1110– 1136, 2006). We introduce a special self-regular proximity to induce the feasibility step and to verify quadratic convergence. The result of polynomial complexity coincides with the best-known iteration bound for infeasib...

When powerful machines such as the Cray-2 became available in the late 1980s, a number of researchers investiWe investigate the use of an inexact Newton’s method to solve the potential equations in the transonic regime. As a test case, gated use of exact Newton’s method for solving steady we solve the two-dimensional steady transonic small disturbance state CFD problems. Direct sparse matrix so...

To efficiently implement implicit Runge-Kutta (IRK) methods for solving large scale stiff ordinary differential equation systems, this paper proposes a new numerical algorithm, which contains a new modified Newton iterative method for solving the nonlinear stage equations of IRK, and two new rules for controlling the updating of Jacobian matrices. A convergence analysis shows that the new modif...

a systematic way is presented for the construction of multi-step iterative method with frozen jacobian. the inclusion of an auxiliary function is discussed. the presented analysis shows that how to incorporate auxiliary function in a way that we can keep the order of convergence and computational cost of newton multi-step method. the auxiliary function provides us the way to overcome the singul...

In this paper, we present SILCA-Newton-Krylov, a new method for accurate, efficient and robust timedomain VLSI circuit simulation. Similar to SPICE, SILCA-Newton-Krylov uses time-difference and Newton-Raphson for solving nonlinear differential equations from circuit simulation. But different from SPICE, SILCA-Newton-Krylov explores a preconditioned flexible generalized minimal residual (FGMRES)...