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Articles 1 - 4 of 4
Full-Text Articles in Numerical Analysis and Computation
A Variable Time-Step Midpoint Scheme For Hamiltonian Systems, Yosi Shibberu
A Variable Time-Step Midpoint Scheme For Hamiltonian Systems, Yosi Shibberu
Mathematical Sciences Technical Reports (MSTR)
A smooth time-step selection formula for the midpoint method is derived which minimize deviations in the Hamiltonian function along piecewise-linear phase space trajectories of autonomous Hamiltonian systems. The time-step formula is implemented in a second order predictor/corrector scheme and applied to Kepler's problem. The formula significantly improves energy conservation as well as the accuracy of the configuration space trajectory. Peak errors in position and momentum coordinates are not significantly reduced, but the time behavior of the errors is markedly more regular.
Multipoint Quadratic Approximation For Numerical Optimization, Michael A. Blaylock
Multipoint Quadratic Approximation For Numerical Optimization, Michael A. Blaylock
Theses and Dissertations
A quadratic approximation for nonlinear functions is developed in order to realize computational savings in solving numerical optimization problems. Function and gradient information accumulated from multiple design points during the iteration history is used in estimating the Hessian matrix. The approximate Hessian matrix is the available for a second order Taylor series approximation to the functions of interest. Several truss and frame models will be used to demonstrate the effectiveness of the new Multipoint Quadratic Approximation (MQA) in solving structural optimization problems.
Automatic Augmented Galerkin Algorithms For Linear First Kind Integral Equations: Non-Singular And Weak Singular Kernels, S. Abbasbandy, E. Babolian
Automatic Augmented Galerkin Algorithms For Linear First Kind Integral Equations: Non-Singular And Weak Singular Kernels, S. Abbasbandy, E. Babolian
Saeid Abbasbandy
In this paper we describe some iterative algorithms for computing these paramteres for non-singular and weak-singular first kind integral equations. We give also error estimates which are easily computed. Finally, we give a number of numerical examples showing that these algorithms work well in practice and netter than methods presented in [2],[3] and [8].
Fixed Points Of Generalized Contractive Multi-Valued Mappings, Peter Z. Daffer, Hideaki Kaneko
Fixed Points Of Generalized Contractive Multi-Valued Mappings, Peter Z. Daffer, Hideaki Kaneko
Mathematics & Statistics Faculty Publications
In a recent paper N. Mizoguchi and W. Takahashi gave a positive answer to the conjecture of S. Reich concerning the existence of fixed points of multi-valued mappings that satisfy a certain contractive condition. In this paper, we provide an alternative and somewhat more straightforward proof for the theorem of Mizoguchi and Takahashi. Also the problems associated with fixed points of weakly contractive multi-valued mappings are studied. Finally, we make a few comments that improve other results from their paper (J. Math. Anal. Appl. 141 (1989), 177-188).