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

Abstract

In this study, discrete fourth order implicit linear multistep methods (LMMs) in block form for the solution of stiff first order initial value problems (IVPs) was presented using power series as a basis and 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, convergence,and accuracy are investigated. The accuracy of the method is tested with two stiff first order initial value problems. The results are compared with fourth order Runge-Kutta (RK4) method, and Berhan et al. (2019). All numerical examples are solved with the aid of MATLAB software and showed that our proposed method produced better accuracy.