Abstract: In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the numerical solution as time is near to maturity.
Abstract: For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.
Abstract: In this paper, we present the preconditioned mixed-type
splitting iterative method for solving the linear systems, Ax = b,
where A is a Z-matrix. And we give some comparison theorems
to show that the convergence rate of the preconditioned mixed-type
splitting iterative method is faster than that of the mixed-type splitting
iterative method. Finally, we give a numerical example to illustrate
our results.
Abstract: In this paper, we present a preconditioned AOR-type iterative method for solving the linear systems Ax = b, where A is a Z-matrix. And give some comparison theorems to show that the rate of convergence of the preconditioned AOR-type iterative method is faster than the rate of convergence of the AOR-type iterative method.
Abstract: From a set of shifted, blurred, and decimated image , super-resolution image reconstruction can get a high-resolution image. So it has become an active research branch in the field of image restoration. In general, super-resolution image restoration is an ill-posed problem. Prior knowledge about the image can be combined to make the problem well-posed, which contributes to some regularization methods. In the regularization methods at present, however, regularization parameter was selected by experience in some cases and other techniques have too heavy computation cost for computing the parameter. In this paper, we construct a new super-resolution algorithm by transforming the solving of the System stem Є=An into the solving of the equations X+A*X-1A=I , and propose an inverse iterative method.
Abstract: In the present paper, we present a modification of the
New Iterative Method (NIM) proposed by Daftardar-Gejji and Jafari
[J. Math. Anal. Appl. 2006;316:753–763] and use it for solving
systems of nonlinear functional equations. This modification yields
a series with faster convergence. Illustrative examples are presented
to demonstrate the method.
Abstract: The paper presents a simple and an accurate formula
that has been developed for the conduction angle (δ) of a single
phase half-wave or full-wave controlled rectifier with RL load. This
formula can be also used for calculating the conduction angle (δ) in
case of A.C. voltage regulator with inductive load under
discontinuous current mode. The simulation results shows that the
conduction angle calculated from the developed formula agree very
well with that obtained from the exact solution arrived from the
iterative method. Applying the developed formula can reduce the
computational time and reduce the time for manual classroom
calculation. In addition, the proposed formula is attractive for real
time implementations.