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Corresponding Author

Atallah El-Shenawy

Subject Area

Mathematics and Engineering Physics

Article Type

Original Study

Abstract

The system of ordinary differential equations arises in many natural phenomena, especially in the field of disease spread. In this paper, a perfect spectral technique is introduced to solve systems of nonlinear differential equations. The technique enhanced the Bessel collocation technique by converting the series notation of unknown variables and their derivatives to matrix relations. The Newton algorithm is developed to solve the resulting nonlinear system of algebraic equations. The effectiveness of the scheme is proved by the convergence analysis and error bound as demonstrated in Theorem 1. The scheme of solution is tested to clarify the efficiency and the high accuracy. The computational part is addressed in the last part of the paper where five problems involve the 1st and 2nd order systems of ordinary differential equations (ODEs). In each case the obtained approximate solution is compared with other numerical and analytical methods. Comparisons were in favour of our solution scheme.

Keywords

Nonlinear systems; Boundary value problems; Bessel polynomials; Newton iterations; Collocation methods.

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

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