Approximate analytical solution of singularly perturbed boundary value problems in MAPLE

Essam R. El-Zahar; Essam R. El-Zahar

doi:10.3934/math.2020150

AIMS Mathematics

2020, Volume 5, Issue 3: 2272-2284. doi: 10.3934/math.2020150

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Research article

Approximate analytical solution of singularly perturbed boundary value problems in MAPLE

Essam R. El-Zahar ^{1,2
,
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1.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
2.
Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom 32511, Egypt

Received: 01 November 2019 Accepted: 19 February 2020 Published: 02 March 2020
MSC : 34B16, 34E15

In this paper, based on a new initial value method, an approximate analytical solution of singularly perturbed boundary value problems is obtained using a new and simple Maple program spivp. The algorithm is designed for practicing engineers or applied mathematicians who need a practical tool for solving these problems. Some examples are solved to illustrate the implementation of the program and the accuracy of the algorithm. Analytical and numerical results are compared with results in literature. The results confirm that the present method is accurate and offers a simple and easy practical tool for obtaining approximate analytical and numerical solutions of singularly perturbed boundary value problems.
- singularly perturbed boundary value problems,
- initial-value algorithms,
- mechanization
Citation: Essam R. El-Zahar. Approximate analytical solution of singularly perturbed boundary value problems in MAPLE[J]. AIMS Mathematics, 2020, 5(3): 2272-2284. doi: 10.3934/math.2020150

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Abstract

In this paper, based on a new initial value method, an approximate analytical solution of singularly perturbed boundary value problems is obtained using a new and simple Maple program spivp. The algorithm is designed for practicing engineers or applied mathematicians who need a practical tool for solving these problems. Some examples are solved to illustrate the implementation of the program and the accuracy of the algorithm. Analytical and numerical results are compared with results in literature. The results confirm that the present method is accurate and offers a simple and easy practical tool for obtaining approximate analytical and numerical solutions of singularly perturbed boundary value problems.

References

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