In this paper, a new step-size skill for a projection and contraction method([10]) for linear programming is generalized to an iterative method([22]) for solving nonlinear projection equation. For linear programming, ...In this paper, a new step-size skill for a projection and contraction method([10]) for linear programming is generalized to an iterative method([22]) for solving nonlinear projection equation. For linear programming, our scheme is the same as that of([10]). For complementarity problem and related problems, we give an improved algorithm by considering the new step-size skill and ALGORITHM B discussed in [22]. Numerical results are provided.展开更多
In this paper, concerned with the Cauchy problem for 2D nonlinear hyperbolic conservation laws,we construct a class of uniformly second order accurate finite difference schemes, which are based on the E-schemes. By ap...In this paper, concerned with the Cauchy problem for 2D nonlinear hyperbolic conservation laws,we construct a class of uniformly second order accurate finite difference schemes, which are based on the E-schemes. By applying the conver gence theorem of Coquel-Le Floch [1], the family of approximate solutions defined by the scheme is proven to converge to the unique entropy weak L∞-solution. Furthermore, some numerical experiments on the Cauchy problem for the advection equation and the Riemann problem for the 2D Burgers equation are given and the relatively satisfied result is obtained.展开更多
In this paper, we consider the numerical solution of quasi-parabolic equations of higher order by a spectral method, and propose a computational formula. We give an error estimate of approximate solutions, and prove t...In this paper, we consider the numerical solution of quasi-parabolic equations of higher order by a spectral method, and propose a computational formula. We give an error estimate of approximate solutions, and prove the convergence of the approximate method and numerical stability on initial values. Under certain conditions, which are much weaker than the conditions in [6], we gain the same convergence rate as in [6].展开更多
文摘In this paper, a new step-size skill for a projection and contraction method([10]) for linear programming is generalized to an iterative method([22]) for solving nonlinear projection equation. For linear programming, our scheme is the same as that of([10]). For complementarity problem and related problems, we give an improved algorithm by considering the new step-size skill and ALGORITHM B discussed in [22]. Numerical results are provided.
文摘In this paper, concerned with the Cauchy problem for 2D nonlinear hyperbolic conservation laws,we construct a class of uniformly second order accurate finite difference schemes, which are based on the E-schemes. By applying the conver gence theorem of Coquel-Le Floch [1], the family of approximate solutions defined by the scheme is proven to converge to the unique entropy weak L∞-solution. Furthermore, some numerical experiments on the Cauchy problem for the advection equation and the Riemann problem for the 2D Burgers equation are given and the relatively satisfied result is obtained.
文摘In this paper, we consider the numerical solution of quasi-parabolic equations of higher order by a spectral method, and propose a computational formula. We give an error estimate of approximate solutions, and prove the convergence of the approximate method and numerical stability on initial values. Under certain conditions, which are much weaker than the conditions in [6], we gain the same convergence rate as in [6].
