A Class of Explicit Integrators with o-grid Interpolation for Solving Non-linear Systems of First Order ODEs
U. W. Sirisena
Department of Mathematics, University of Jos, Nigeria.
S. I. Luka *
Department of Mathematics, University of Jos, Nigeria.
S. Y. Yakubu
Department of Mathematics and Computer Science, Federal University Kashere, Gombe, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This research work is aimed at constructing a class of explicit integrators with improved stability and accuracy by incorporating an off-gird interpolation point for the purpose of making them effcient for solving stiff initial value problems. Accordingly, continuous formulations of a class of hybrid explicit integrators are derived using multi-step collocation method through matrix inversion technique, for step numbers k = 2; 3; 4: The discrete schemes were deduced from their respective continuous formulations. The stability and convergence analysis were carried out and shown to be A(α)-stable and convergent respectively. The discrete schemes when implemented as block integrators to solve some non-linear problems, it was observed that the results obtained compete favorably with the MATLAB ode23 solver.
Keywords: Block, Hybrid, Explicit integrators, off-gird interpolation, continuous formulation.