In this paper, the multigrid algorithm was used to solve Poisson’s equation for various right-hand sides. However, in order to calculate the discretized laplacian value, both a second-order and a fourth-order laplacian operator was used. The fourth-order laplacian operator achieves higher accuracy at the cost of more calculations and a longer execution time. In order to compensate for this, the...

Integrating various suppliers to satisfy market demand is of great importance for e ective supply chain management. In this paper, we consider the ODE-PDE model of supply chain and apply a classical explicit fourth-order Runge-Kutta scheme for the related ODE model of suppliers. Also, the convergence of the proposed method is proved. Finally a numerical example is studied to demonstrate the acc...

In this paper, a variable-order nonlinear cable equation is considered. The numerical method with first order temporal accuracy and fourth order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second order temporal accuracy and fourth order spatial accuracy. Finally, the resul...

To integrate large systems of ordinary differential equations (ODEs) with disparate timescales, we present a multirate method with error control that is based on embedded, explicit Runge-Kutta (RK) formulas. The order of accuracy of such methods depends on interpolating certain solution components with a polynomial of sufficiently high degree. By analyzing the method applied to a simple test eq...

In this paper, we propose a dynamic B-spline technique using general form fourth order geometric PDEs. Basing on discretizaions of Laplace-Beltrami operator and Gaussian curvature over triangular and quadrilateral meshes and their convergence analysis, we propose in this paper a novel approach for constructing geometric PDE B-spline surfaces, using general form fourth order geometric flows. Fou...

In this article, we suggest the local analysis of a uni-parametric third and fourth order class iterative algorithms for addressing nonlinear equations in Banach spaces. The proposed convergence is established using an ω-continuity condition on first Fréchet derivative. way, utility discussed schemes extended application Taylor expansion removed. Furthermore, study provides radii balls uniquene...

Fourth-order stream-function methods are proposed for the time dependent, incompressible Navier-Stokes and Boussinesq equations. Wide difference stencils are used instead of compact ones and the boundary terms are handled by extrapolating the stream-function values inside the computational domain to grid points outside, up to fourth-order in the noslip condition. Formal error analysis is done f...

We present a fourth order compact nite diierence scheme on the face centered cubic (FCC) grids for the numerical solution of the two dimensional convection diiusion equation. The seven point formula is deened on a regular hexagon, where the strategy of directional derivative is employed to make the derivation procedure straightforward, eecient, and concise. A corresponding multigrid method is d...

The complete set of second-, third-, and fourth-order van der Waals coefficients Cn up to n=32 for the Hs1sd-Hs1sd dimer have been determined. They are computed by diagonalizing the nonrelativistic Hamiltonian for hydrogen to obtain a set of pseudostates that are used to evaluate the appropriate sum rules. A study of the convergence pattern for nø16 indicates that all the Cnø16 coefficients are...