Development And Application Of Multi-Derivative Hybrid Block Methods For Solving Nonlinear First-Order Ordinary Differential Equations
DOI:
https://doi.org/10.60787/tnamp.v21.470Keywords:
Numerical technique , Hybrid-point, Non-linear dynamical system, Block Method, Multi-derivative methodAbstract
In this paper, two step implicit hybrid block multistep method, incorporating multi-derivatives is considered. The first incorporated second, third and fourth derivative, while the second incorporated second, third, fourth derivative and fifth derivative. The schemes are generated for the numerical solution of non-linear dynamical first order ordinary differential equations. The study made use of Bhaskara cosine approximation formula to generate hybrid points for the optimization of the numerical schemes generated by using collocation and interpolation technique. Power series is used as the basis function in approximating the solution. The methods are self-starting, of higher order, zero-stable, consistent and are A-stable. The methods are used to solve problems from chaos theory, SIR-model and multi-dimension problem to demonstrate the effectiveness of the method and its ability provide reliable solutions over existing methods.
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