In this paper the Schwarz alternating method for a fourth-order elliptic variational inequality problem is considered by way of the equivalent form, and the geometric convergence is obtained on two subdomains.
In a recent paper, Noor and Khan [M. Aslam Noor, & W. A. Khan, (2012) New Iterative Methods for Solving Nonlinear Equation by Using Homotopy Perturbation Method, Applied Mathematics and Computation, 219, 3565-3574...In a recent paper, Noor and Khan [M. Aslam Noor, & W. A. Khan, (2012) New Iterative Methods for Solving Nonlinear Equation by Using Homotopy Perturbation Method, Applied Mathematics and Computation, 219, 3565-3574], suggested a fourth-order method for solving nonlinear equations. Per iteration in this method requires two evaluations of the function and two of its first derivatives;therefore, the efficiency index is 1.41421 as Newton’s method. In this paper, we modified this method and obtained a family of iterative methods for appropriate and suitable choice of the parameter. It should be noted that per iteration for the new methods requires two evaluations of the function and one evaluation of its first derivatives, so its efficiency index equals to 1.5874. Analysis of convergence shows that the methods are fourth-order. Several numerical examples are given to illustrate the performance of the presented methods.展开更多
In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state （EOS） for pure substance. The mas...In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state （EOS） for pure substance. The mass conservation, energy decay property, unique solvability and L~ convergence of these two schemes are proved. Numerical results demon- strate the good approximation of the fourth order equation and confirm reliability of these two schemes.展开更多
文摘In this paper the Schwarz alternating method for a fourth-order elliptic variational inequality problem is considered by way of the equivalent form, and the geometric convergence is obtained on two subdomains.
文摘In a recent paper, Noor and Khan [M. Aslam Noor, & W. A. Khan, (2012) New Iterative Methods for Solving Nonlinear Equation by Using Homotopy Perturbation Method, Applied Mathematics and Computation, 219, 3565-3574], suggested a fourth-order method for solving nonlinear equations. Per iteration in this method requires two evaluations of the function and two of its first derivatives;therefore, the efficiency index is 1.41421 as Newton’s method. In this paper, we modified this method and obtained a family of iterative methods for appropriate and suitable choice of the parameter. It should be noted that per iteration for the new methods requires two evaluations of the function and one evaluation of its first derivatives, so its efficiency index equals to 1.5874. Analysis of convergence shows that the methods are fourth-order. Several numerical examples are given to illustrate the performance of the presented methods.
文摘In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state （EOS） for pure substance. The mass conservation, energy decay property, unique solvability and L~ convergence of these two schemes are proved. Numerical results demon- strate the good approximation of the fourth order equation and confirm reliability of these two schemes.
基金The National Science Foundation of China(10701066)Basic and Cutting-edge Technology Research Projects of Henan Province (092300410137)+1 种基金The Natural Science Foundation of Henan Education Committee(2008-755-65)The NationalScience Foundation of the Education Department of Henan province (2008A110022)
