Abstract: An inversion-free iterative algorithm is presented for
solving nonlinear matrix equation with a stepsize parameter t. The
existence of the maximal solution is discussed in detail, and the
method for finding it is proposed. Finally, two numerical examples
are reported that show the efficiency of the method.
Abstract: An important task in solving second order linear ordinary differential equations by the finite difference is to choose a suitable stepsize h. In this paper, by using the stochastic arithmetic, the CESTAC method and the CADNA library we present a procedure to estimate the optimal stepsize hopt, the stepsize which minimizes the global error consisting of truncation and round-off error.
Abstract: This paper considers the development of a two-point
predictor-corrector block method for solving delay differential
equations. The formulae are represented in divided difference form
and the algorithm is implemented in variable stepsize variable order
technique. The block method produces two new values at a single
integration step. Numerical results are compared with existing
methods and it is evident that the block method performs very well.
Stability regions of the block method are also investigated.
Abstract: In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented.
Abstract: This paper presents the determination of the proper
quality costs parameters which provide the optimum return. The
system dynamics simulation was applied. The simulation model was
constructed by the real data from a case of the electronic devices
manufacturer in Thailand. The Steepest Descent algorithm was
employed to optimise. The experimental results show that the
company should spend on prevention and appraisal activities for 850
and 10 Baht/day respectively. It provides minimum cumulative total
quality cost, which is 258,000 Baht in twelve months. The effect of
the step size in the stage of improving the variables to the optimum
was also investigated. It can be stated that the smaller step size
provided a better result with more experimental runs. However, the
different yield in this case is not significant in practice. Therefore, the
greater step size is recommended because the region of optima could
be reached more easily and rapidly.