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Onumanyi, P.A., Awoyemi, D., Jator, S.N. and Sirisena U.W. (1994) New Linear Multi-Step Methods with Continuous Coefficients for First Order Initial Value Problems. Journal of the Nigerian Mathematical Society, 13, 37-51.

has been cited by the following article:

• TITLE: A Class of Hybrid Explicit Integrators (HEI) with Off-Grid Collocation for Solving Non-Linear Systems of First Order ODEs

  AUTHORS: Sunday Izang Luka, Wipuni Sirisena, Oludare Adedire

  KEYWORDS: Block, Hybrid, Explicit Integrators, Off-Grid Collocation, Continuous Formulation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.5, May 29, 2026

  ABSTRACT: In this paper, we aim at improving the stability and accuracy of the explicit methods by incorporating off-grid collocation for the purpose of making them efficient for solving stiff nonlinear problems. As such, continuous formulation of a class of hybrid explicit integrators are derived using multi-step collocation method through matrix inversion technique. This involves off-grid point at collocation for step numbers k = 2, 3, 4 hence discrete schemes were deduced from their respective continuous formulations. The stability analysis indicates that HEIs for k = 2, 3, 4 are Lo-stable. Also, convergence analysis was carried out and all HEIs are shown to be convergent. The discrete schemes were tested as block integrators on some non-linear systems of first order ODEs, and the results show that the new HEIs are efficient and compete favourably with the ode23s solver in MATLAB.