CONSTRUCTING THE IMPLIMENTATION TO THE CONTINUOUS BLOCK BDF METHODS

Abstract

The k-step methods of continuous block backward difference formula (or BDF) have great benefit to approximate the differential equation with the initial condition. These methods possessing very large absolute stability regions are especially useful for the stiff equations. This article presents a method of implementation to these k-step scheme by using the Newton’s iteration for the root finding problem of the non-linear multivariable case. Also, a program written in Matlab with a particular k is presented. The numerical experiments introduced to illustrate the efficiency and exactness of these scheme comparing with some conventional BDF methods.