Fourth-order compact schemes with adaptive time step for monodomain reaction–diffusion equations

High Order Compact Finite Difference Schemes for Solving Bratu-Type Equations

In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the ...

Fourth Order Schemes for Time-Harmonic Wave Equations with Discontinuous Coefficients

We consider high order methods for the one-dimensional Helmholtz equation and frequency-Maxwell system. We demand that the scheme be higher order even when the coefficients are discontinuous. We discuss the connection between schemes for the second-order scalar Helmholtz equation and the first-order system for the electromagnetic or acoustic applications. AMS subject classifications: 65N06, 78A...

Fourth-Order Compact Schemes for Solving Multidimensional Heat Problems with Neumann Boundary Conditions

In this article, two sets of fourth-order compact finite difference schemes are constructed for solving heatconducting problems of two or three dimensions, respectively. Both problems are with Neumann boundary conditions. These works are extensions of our earlier work (Zhao et al., Fourth order compact schemes of a heat conduction problemwith Neumann boundary conditions, NumericalMethods Partia...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

Convergence Analysis of High Order Algebraic Fractional Step Schemes for Time-Dependent Stokes Equations

In this paper we analyze the family of Yosida algebraic fractional step schemes proposed in [A. Quarteroni, F. Saleri, and A. Veneziani, Comput. Methods Appl. Mech. Engrg., 188 (2000), pp. 505–526], [F. Saleri and A. Veneziani, SIAM J. Numer. Anal., 43 (2005), pp. 174–194], and [P. Gervasio, F. Saleri, and A. Veneziani, J. Comput. Phys., 214 (2006), pp. 347–365] when applied to time-dependent S...