In this paper, we consider the development of an extended block integrator for the solution of stiff and oscillatory first-order Ordinary Differential Equations (ODEs) using interpolation and collocation techniques. The integrator was developed by collocation and interpolation of the combination of power series and exponential function to generate a continuous implicit Linear Multistep Method (LMM). The paper further investigates the basic properties of the block integrator and found it to be zero-stable, consistent and convergent. The integrator was also tested on some sampled stiff and oscillatory problems and found to perform better than some existing ones.
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