(a) Comparison of the approximate solution with the exact solution for the example 2.

<p>(b) Absolute error of example 2. (c) Relative error of example 2.</p>

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Bibliographic Details
Main Author:	Lahoucine Tadoummant (21647670) (author)
Other Authors:	Hammad Khalil (21647673) (author), Rachid Echarggaoui (21647676) (author), Sarah Aljohani (6882797) (author), Nabil Mlaiki (21213249) (author)
Published:	2025
Subjects:	Space Science Biological Sciences not elsewhere classified Mathematical Sciences not elsewhere classified sup >&# 8722 relative errors decreased performed using matlab nonlocal boundary condition local boundary conditions ></ sub >\|. ></ sub >\|, >< sub >< exponential convergence behavior convergence rates lie shifted legendre polynomials new operational matrices matlab codes used div >< p relative error \|< proposed numerical method proposed method shows 1 </ sup error types proposed method proposed approach novel method x </ significant reduction rigorously analyzed results obtained results confirm r </ pseudo code high precision effectively handles coupled systems computational examples algebraic equations
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