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

In this paper, discrete implicit linear multistep methods in block form for the solution of initial valueproblems was presented using the Chebyshev polynomials. The method is based on collocation of thedifferential 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 assimultaneous numerical integrators to form block method. The basic properties of the method such asorder, error constant, zero stability, consistency and accuracy are investigated. The accuracy of themethod was tested with two stiff first order initial value problems. The results were compared with amethod reported in the literature. All numerical examples were solved with the aid of MATLABsoftware after the schemes are developed using MAPLE software and the results showed that ourproposed method produces better results.