Block Procedure for Solving Stiff First Order Initial Value Problems Using Chebyshev Polynomials

Abstract

In this paper, discrete implicit linear multistep methods in block form for the solution of initial value
problems was presented using the Chebyshev polynomials. The method is based on collocation of the
differential equation and interpolation of the approximate solution of power series at the grid points.
The procedure yields four consistent implicit linear multistep schemes which are combined as
simultaneous numerical integrators to form block method. The basic properties of the method such as
order, error constant, zero stability, consistency and accuracy are investigated. The accuracy of the
method was tested with two stiff first order initial value problems. The results were compared with a
method reported in the literature. All numerical examples were solved with the aid of MATLAB
software after the schemes are developed using MAPLE software and the results showed that our
proposed method produces better results.