In this paper we construct a new third-order iterative method for solving nonlinear equations for simple roots by using inverse function theorem. After that a class of optimal fourth-order methods by using one function and two first derivative evaluations per full cycle is given which is obtained by improving the existing third-order method with help of weight function. Some physical examples a...

The Cahn-Hilliard equation has its origin in material sciences and serves as a model for phase separation and phase coarsening in binary alloys. A new approach in the class of fourth order inpainting algorithms is inpainting of binary images using the Cahn-Hilliard equation. We will present a generalization of this fourth order approach for grayvalue images. This is realized by using subgradien...

We note in this study that the Navier-Stokes equations, when expressed in streamfunction-vorticity fonn, can be approximated to fourth--order accuracy with stencils extending only over a 3 x 3 square of points. The key advantage of the new compact fourth-order scheme is that it allows direct iteration for low~to-mediwn Reynolds numbers. Numerical solutions are obtained for the model problem of ...

In the proposed method, the variation of displacement in each time step is assumed to be a fourth order polynomial in time and its five unknown coefficients are calculated based on: two initial conditions from the previous time step; satisfying the equation of motion at both ends of the time step; and the zero weighted residual within the time step. This method is non-dissipative and its disper...

In this paper, a high-order and fast numerical method is investigated for the time-fractional Black-Scholes equation. order to deal with typical weak initial singularity of solution, we construct finite difference scheme variable time steps, where fractional derivative approximated by nonuniform Alikhanov formula sum-of-exponentials (SOE) technique. spatial direction, an average approximation f...

A fractional trapezoidal rule type difference scheme for fractional order integro-differential equation is considered. The equation is discretized in time by means of a method based on the trapezoidal rule: while the time derivative is approximated by the standard trapezoidal rule, the integral term is discretized by means of a fractional quadrature rule constructed again from the trapezoidal r...

We present two fourth-order compact finite difference (CFD) discretizations of the velocity-pressure formulation of the acoustic wave equation in 2-D rectangular grids. The first method uses standard implicit CFD on nodal meshes and requires solving tridiagonal linear systems along each grid line, while the second scheme employs a novel set of mimetic CFD operators for explicit differentiation ...

The numerical simulation of the dynamics of the molecular beam epitaxy (MBE) growth is considered in this article. The governing equation is a nonlinear evolutionary equation that is of linear fourth order derivative term and nonlinear second order derivative term in space. The main purpose of this work is to construct and analyze two linearized finite difference schemes for solving the MBE mod...

Using the Dirac constraint method we show that the pure fourth-order PaisUhlenbeck oscillator model is free of observable negative norm states. Even though such ghosts do appear when the fourth order theory is coupled to a second order one, the limit in which the second order action is switched off is found to be a highly singular one in which these states move off shell. Given this result, con...

Singularly perturbed boundary value problem can be solved using various techniques. The solution of the following fourth order self adjoint singularly perturbed boundary value problem is approximated using quintic spline Ly = − y(4) + p(x)y = f(x), p(x) ≥ p > 0, y(a) = α0, y(b) = α1, y(1)(a) = α2, y(1)(b) = α3, } or Ly = − y(4) + p(x)y = f(x), p(x) ≥ p > 0, y(a) = α0, y(b) = α1, y(2)(a) = α4, y...