In this paper, we study an efficient asymptotically correction of a-posteriori er- ror estimator for the numerical approximation of Volterra integro-differential equations by piecewise polynomial collocation method. T...In this paper, we study an efficient asymptotically correction of a-posteriori er- ror estimator for the numerical approximation of Volterra integro-differential equations by piecewise polynomial collocation method. The deviation of the error for Volterra integro- differential equations by using the defect correction principle is defined. Also, it is shown that for m degree piecewise polynomial collocation method, our method provides O（hm＋l） as the order of the deviation of the error. The theoretical behavior is tested on examples and it is shown that the numerical results confirm the theoretical part.展开更多
In this paper, we correct the Stefan–Boltzmann law by considering the generalized uncertainty principle, and with this corrected Stefan–Boltzmann law, the lifespan of the Schwarzschild-de-sitter black holes is calcu...In this paper, we correct the Stefan–Boltzmann law by considering the generalized uncertainty principle, and with this corrected Stefan–Boltzmann law, the lifespan of the Schwarzschild-de-sitter black holes is calculated. We find that the corrected Stefan–Boltzmann law contains two terms, the 46 Tterm and the Tterm. Due to the modifications, at the end of the black hole radiation, it will arise a limited highest temperature and leave a residue. It is interesting to note that the mass of the residue and the Planck mass is in the same order of magnitude. The modified Stefan–Boltzmann law also gives a correction to the lifespan of the black hole, although it is very small.展开更多
文摘In this paper, we study an efficient asymptotically correction of a-posteriori er- ror estimator for the numerical approximation of Volterra integro-differential equations by piecewise polynomial collocation method. The deviation of the error for Volterra integro- differential equations by using the defect correction principle is defined. Also, it is shown that for m degree piecewise polynomial collocation method, our method provides O（hm＋l） as the order of the deviation of the error. The theoretical behavior is tested on examples and it is shown that the numerical results confirm the theoretical part.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11273009 and 11303006
文摘In this paper, we correct the Stefan–Boltzmann law by considering the generalized uncertainty principle, and with this corrected Stefan–Boltzmann law, the lifespan of the Schwarzschild-de-sitter black holes is calculated. We find that the corrected Stefan–Boltzmann law contains two terms, the 46 Tterm and the Tterm. Due to the modifications, at the end of the black hole radiation, it will arise a limited highest temperature and leave a residue. It is interesting to note that the mass of the residue and the Planck mass is in the same order of magnitude. The modified Stefan–Boltzmann law also gives a correction to the lifespan of the black hole, although it is very small.
