RIGOROUS ANALYSIS OF A HIGHLY EFFICIENT THIRD-ORDER INTEGRATOR FOR INITIAL VALUE PROBLEMS
DOI:
https://doi.org/10.71146/kjmr915Keywords:
Local Truncation Error, Stability, Consistency, ConvergenceAbstract
In this paper, we have theoretically studied well-organized third order numerical technique of IVP of ODE including partial derivative that has improved its competency in light of truncation error. Theoretically, integrator method of local truncation error and convergence is studied, to determine how precise and trustworthy proposed method is. Expansion of the series of Taylor is carried out that offers suitable pattern to expand and analyze function evaluation. Local truncation error, aiding with the series developed by Taylor, is an explicitly stated error to explain the order of accuracy. Linear standard test is taken in calculating the stability. Knowing behavior of method is explored under the stability. MATLAB2023a software is used to draw stability region. Stability region is also visualized to verify that the numerical method has a solution that is limited when used repeatedly and very frequently. Consistency is demonstrated that informs us that error decreases to zero as much as we shrink step size which ensures desired outcome. Convergence criteria are theoretically discussed here by proving consistency and stability. Theoretical results proving that the numerical method is stable, achieves high accuracy and provides a reliable performance. Hence, method is effective and can be used in the general class of IVP that occur in the field of ODE.
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Copyright (c) 2026 Muhammad Daud Kandhro, Sobia Vighio, Asad Ali khore (Author)
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