In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems arise, e.g., from the outer convexification of integer control decisions. We treat this optimal control problem class using the direct multiple shooting method to discretize the optimal control problem. The resulting nonlinear problems are solved using sequen...

Probe insertion technique is considered as an exclusively frequency domain approach. It has been developed to increase robustness of the harmonic balance method, when simulating autonomous circuits to avoid the DC degenerate solution. This technique evidences several good properties, for instance when simulating oscillators either employing high quality factor resonators or AC coupled ones. In ...

This paper presents a gathering and shooting progressive refinement radiosity method. Our method integrates the iterative process of light energy gathering used in the standard full matrix method and the iterative process of light energy shooting used in the conventional progressive refinement method. As usual, in each iteration, the algorithm first selects the patch which holds the maximum unp...

The present study examines embedded open parallel microchannels within a micropatterned permeable surface for reducing entropy generation in MHD fluid flow in microscale systems. A local similarity solution for the transformed governing equations is obtained. The governing partial differential equations along with the boundary conditions are first cast into a dimensionless form and then the red...

This paper gives a brief list of commonly used direct and indirect efficient methods for the numerical solution of optimal control problems. To improve the low accuracy of the direct methods and to increase the convergence areas of the indirect methods we suggest a hybrid approach. For this a special direct collocation method is presented. In a hybrid approach this direct method can be used in ...

In this paper, we present a variational integrator that is based on an approximation of the Euler–Lagrange boundary-value problem via Taylor’s method. This can be viewed as a special case of the shooting-based variational integrator. The Taylor variational integrator exploits the structure of the Taylor method, which results in a shooting method that is one order higher compared to other shooti...

In this report, the raypath equation is deduced by using plane wave theory and making high frequency approximation. Two kinds of two-point seismic ray tracing iterative nonlinear methods(the Shooting method and the Bending method) are discussed. The Shooting method fixes one end and apply the raypath equation to find the ray path. The Bending method fixes both ends and use Fermat’s principle to...

1 In this paper, a modified Steffensen's type iterative scheme for the numerical solution of a system of nonlinear equations is studied. Two convergence theorems are presented. The numerical solution of boundary-value problems by the multiple shooting method using the proposed iterative scheme is analyzed. A unified approach for enlarging the radius of convergence for Newton's method and applic...

A novel method based on Genetic Algorithm to solve the boundary value problems (BVPs) of the Falkner–Skan equation over a semi-infinite interval has been presented. In our approach, we use the free boundary formulation to truncate the semi-infinite interval into a finite one. Then we use the shooting method based on Genetic Algorithm to transform the BVP into initial value problems (IVPs). Gene...