Chebyshevian basis function-type block method for the solution of first-order initial value problems with oscillating solutions

Abstract

In this paper, we develop a block method using Chebyshev polynomial basis function and use it to produce discrete methods which are simultaneously applied as numerical integrators by assembling them into a block method. The paper further investigates the properties of the block method and found it to be zero-stable, consistent and convergent. We also tested the efficiency of the method on some sampled oscillatory problems and found out that the method performed better than some existing ones with which we compared our results.