In this paper we provide an analysis of monotonicity properties for linear multistep methods. These monotonicity properties include positivity and the diminishing of total variation. We also pay particular attention to related boundedness properties such as the total variation bounded (TVB) property. In the analysis the multistep methods are considered in combination with suitable starting proc...

in this paper, a new spectral-iterative method is employed to give approximate solutions of fractional logistic differential equation. this approach is based on combination of two different methods, i.e. the iterative method cite{35} and the spectral method. the method reduces the differential equation to systems of linear algebraic equations and then the resulting systems are solved by a numer...

. In this paper, we develop a quadratic spline collocation method for integrating the nonlinear partial differential equations (PDEs) of a plug flow reactor model. The method is proposed in order to be used for the operation of control design and/or numerical simulations. We first present the Crank-Nicolson method to temporally discretize the state variable. Then, we develop and analyze the pro...

In this paper, a Chebyshev spectral collocation domain decomposition (DD) semidiscretization by using a grid mapping, derived by Kosloff and Tal-Ezer in space is applied to the numerical solution of the generalized Burger’s–Huxley (GBH) equation. To reduce roundoff error in computing derivatives we use the above mentioned grid mapping. In this work, we compose the Chebyshev spectral collocation...

We propose a discrete collocation method for the boundary integral equations which arise from solving Laplace's equation u = 0. The Laplace's equation is deened on connected regions D in R 3 with a smooth boundary S. The piecewise polynomial interpolation in the parametrization variables along with the collocation method is used, and a numerical integration scheme for collocation integrals is g...

in this paper we use radial basis functions to solve multivariable integral equations. we use collocation method for implementation. numerical experiments show the accuracy of the method.

by Margaret Adams. Heinemann. 25s. Work with the mentally subnormal has always demanded a high degree of skill and the failure to recognise this reflects society's attitude to the handicap. This attitude is fortunately in process of being modified and Margaret Adams is to be congratulated on bringing together a team of people who can speak with such authority of the rewarding nature of work wit...

This paper summarizes things the author considers important from his past work, and presents some new ideas for use in the implementation of multistep methods. An eeort has been made to include material of interest to those of a theoretical bent, as well as to those whose primary interest is in the implementation of methods.