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Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 14 Issue: 1

Modified Finite Difference Method for Solution of Two-interval Boundary Value Problems with Transition Conditions

Semih Çavuşoğlu(TOKAT GAZİOSMANPAŞA ÜNİVERSİTESİ)0000-0002-8194-4008
Oktay Mukhtarov(TOKAT GAZİOSMANPAŞA ÜNİVERSİTESİ)0000-0001-7480-6857
Pages
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Publication Date
2022-06-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Corresponding graphical illustration are also presented.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we have proposed a new modification of classical Finite Difference Method (FDM) for the solution of boundary value problems which are defined on two disjoint intervals and involved additional transition conditions at an common end of these intervals.
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Key Findings & Data:To illustrate the efficiency and reliability of the proposed modification of FDM some examples are solved.
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Conclusion & Impact:Corresponding graphical illustration are also presented.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Finite difference method · transition conditions · boundary value problem

Abstract

In this study, we have proposed a new modification of classical Finite Difference Method (FDM) for the solution of boundary value problems which are defined on two disjoint intervals and involved additional transition conditions at an common end of these intervals. The proposed modification of FDM differs from the classical FDM in calculating the iterative terms of numerical solutions. To illustrate the efficiency and reliability of the proposed modification of FDM some examples are solved. The obtained results are compared with those obtained by the standart FDM and by the analytical method. Corresponding graphical illustration are also presented.

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Cite This Article

Çavuşoğlu, S., Mukhtarov, O. (2022). Modified Finite Difference Method for Solution of Two-interval Boundary Value Problems with Transition Conditions. Turkish Journal of Mathematics and Computer Science, Volume: 14 Issue: 1. https://doi.org/10.47000/tjmcs.1007380

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References (16)

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