Current Issue : January - March Volume : 2018 Issue Number : 1 Articles : 5 Articles
In this paper, we propose an efficient numerical scheme for the approximate solution\nof a time fractional diffusion-wave equation with reaction term based on cubic\ntrigonometric basis functions. The time fractional derivative is approximated by the\nusual finite difference formulation, and the derivative in space is discretized using\ncubic trigonometric B-spline functions. A stability analysis of the scheme is conducted\nto confirm that the scheme does not amplify errors. Computational experiments are\nalso performed to further establish the accuracy and validity of the proposed scheme.\nThe results obtained are compared with finite difference schemes based on the\nHermite formula and radial basis functions. It is found that our numerical approach\nperforms superior to the existing methods due to its simple implementation,\nstraightforward interpolation and very low computational cost. A convergence\nanalysis of the scheme is also discussed....
A new algorithm is proposed for polynomial or rational approximation of the planar\noffset curve. The best rational Chebyshev approximation could be regarded as a kind of geometric\napproximation along the fixed direction. Based on this idea, we developed a wholly new offset\napproximation method by changing the fixed direction to the normal directions. The error vectors\nfollow the direction of normal, and thus could reflect the approximate performance more properly.\nThe approximation is completely independent of the original curve parameterization, and thus\ncould ensure the stability of the approximation result. Experimental results show that the proposed\nalgorithm is reasonable and effective....
The idea of the normalisation of the Hamiltonian system is to simplify the system by\ntransforming Hamiltonian canonically to an easy system. It is under symplectic conditions that the\nHamiltonian is preserved under a specific transformationââ?¬â?the so-called Lie transformation. In this\nreview, we will show how to compute the normal form for the Hamiltonian, including computing\nthe general function analytically. A clear example has been studied to illustrate the normal form\ntheory, which can be used as a guide for arbitrary problems...
This paper addresses the unrelated parallel machines scheduling problem with sequence and machine dependent setup times. Its\ngoal is to minimize the makespan. The problem is solved by a combinatorial Benders decomposition. This method can be slow to\nconverge.Therefore, three procedures are introduced to accelerate its convergence.The first procedure is a newmethod that consists\nof terminating the execution of the master problem when a repeated optimal solution is found.The second procedure is based on\nthemulticut technique.The third procedure is based on the warm-start.Theimproved Benders decomposition scheme is compared\nto a mathematical formulation and a standard implementation of Benders decomposition algorithm. In the experiments, two test\nsets from the literature are used, with 240 and 600 instances with up to 60 jobs and 5 machines. For the first set the proposed\nmethod performs 21.85% on average faster than the standard implementation of the Benders algorithm. For the second set the\nproposed method failed to find an optimal solution in only 31 in 600 instances, obtained an average gap of 0.07%, and took an\naverage computational time of 377.86 s, while the best results of the other methods were 57, 0.17%, and 573.89 s, respectively....
The exponentially-distributed random timestepping algorithm with boundary\ntest is implemented to evaluate the prices of some variety of single one-sided\nbarrier option contracts within the framework of Black-Scholes model, giving\nefficient estimation of their hitting times. It is numerically shown that this algorithm,\nas for the Brownian bridge technique, can improve the rate of weak\nconvergence from order one-half for the standard Monte Carlo to order 1.\nThe exponential timestepping algorithm, however, displays better results, for\na given amount of CPU time, than the Brownian bridge technique as the step\nsize becomes larger or the volatility grows up. This is due to the features of the\nexponential distribution which is more strongly peaked near the origin and\nhas a higher kurtosis compared to the normal distribution, giving more stability\nof the exponential timestepping algorithm at large time steps and high levels\nof volatility....
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