Abstract
In this paper, new approximation methods for solving systems of ordinary differential equations (SODEs) by fuzzy transform (FzT) are introduced and discussed. In particular, we propose two modified numerical schemes to solve SODEs where the technique of FzT is combined with one-stage and two-stage numerical methods. Moreover, the error analysis of the new approximation methods is discussed. Finally, numerical examples of the proposed approach are confirmed, and applications are presented.
Highlights
Differential equations have great potential to model and understand real-world problems in science and engineering
fuzzy transform (FzT) was proposed for numerical solutions of two point boundary value problems by the more efficient way in comparison with the similar ones obtained by the finite difference method [9]
In view of the methodological remarks in Subsection 3.1, we describe the complete sequence of steps, which leads to the approximation solution of systems of ordinary differential equations (SODEs) (5)
Summary
Differential equations have great potential to model and understand real-world problems in science and engineering. In [19], new fuzzy methods based on FzT for solving the Cauchy problem were presented, and the authors compared the results with existing numerical results in [6,32] and with classical methods, including one, two and three steps. All these fuzzy approximation methods performed better than the classical trapezoidal rule (one step) and the classical Adam–Moulton method (two and three steps) and outperformed the previous fuzzy methods in [6,32].
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