Abstract: In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.
Abstract: This paper presents the development, analysis and
implementation of an inverse polynomial numerical method which is
well suitable for solving initial value problems in first order ordinary
differential equations with applications to sample problems. We also
present some basic concepts and fundamental theories which are vital
to the analysis of the scheme. We analyzed the consistency,
convergence, and stability properties of the scheme. Numerical
experiments were carried out and the results compared with the
theoretical or exact solution and the algorithm was later coded using
MATLAB programming language.