To justify the effectiveness of the presented generalization of DTM, we solved two MIBVTPs for the three-interval differential equations and graphically compared the obtained approximate solutions with the corresponding exact solutions.
📌 3 Key Takeaways
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Objective & Hypothesis:Although the well-known differential transform method (DTM) is one of the effective methods for solving single-interval boundary value problems (SIBVPs), this method cannot be directly applied to multi-intervalboundary value transmission problems (MIBVTPs).
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Key Findings & Data:In this study, we generalized the classical DTM so that it can be applied to solving not only SIBVPs but also MIBVTPs.
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Conclusion & Impact:To justify the effectiveness of the presented generalization of DTM, we solved two MIBVTPs for the three-interval differential equations and graphically compared the obtained approximate solutions with the corresponding exact solutions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Ordinary differential equations · boundary value problems · transmission conditions
Abstract
Although the well-known differential transform method (DTM) is one of the effective methods for solving single-interval boundary value problems (SIBVPs), this method cannot be directly applied to multi-intervalboundary value transmission problems (MIBVTPs). In this study, we generalized the classical DTM so that it can be applied to solving not only SIBVPs but also MIBVTPs. To justify the effectiveness of the presented generalization of DTM, we solved two MIBVTPs for the three-interval differential equations and graphically compared the obtained approximate solutions with the corresponding exact solutions.
Yücel, M., Muhtarov, F., Mukhtarov, O. (2024). Modification of DTM for Solving Multi-Interval Boundary Value Problems. Turkish Journal of Mathematics and Computer Science, Volume: 16 Issue: 2. https://doi.org/10.47000/tjmcs.1550305
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