This paper demonstrates a new approach to handle ordinary differential equations using spectral collocation methods and operational matrices for improved accuracy.
This paper presents a novel numerical approach to handling ordinary differential equations (ODEs) with initial conditions (ICs) by introducing generalized exponential Jacobi functions (GEJFs). These GFJFs satisfy the associated ICs. A crucial part of this approach is using the spectral collocation method (SCM) and building operational matrices (OMs) for the ordinary derivatives (ODs) of GEJFs. These lead to efficient and accurate computations. The suggested algorithm’s convergence and error analysis is proved. We present numerical examples to demonstrate the applicability of the approach.
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H. M. Ahmed (2025) studied this question.
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