**Title:** Sin single-step rational method for the numerical solution of initial value problems

**Montes Taurus J. Pure Appl. Math.** / ISSN: 2687-4814

**Article ID:** MTJPAM-D-22-00004; **Volume 5 / Issue 2 / Year 2023**, Pages 6-15

**Document Type:** Research Paper

**Author(s):** Pramod Kumar Pandey ^{a} , Sathyendar Sreepada ^{b}

^{a}Department of Mathematics, Dyal Singh College (University of Delhi), Lodhi Road, New Delhi-110003, India

^{b}Mathematics Unit, School of Foundation, Bahrain Polytechnic, Isa Town, PO Box-33349, Kingdom of Bahrain

Received: 16 February 2022, Accepted: 26 September 2023, Published: 25 October 2023

**Corresponding Author:** Pramod Kumar Pandey (Email address: pramod_10p@hotmail.com)

**Full Text:** PDF

**Abstract**

In this article, a sin single-step rational method for the numerical numerical solution of the first order differential equation and corresponding initial value problems has been proposed. Also, the consistency and stability of the proposed second order implicit, non-linear method are discussed. The development of the method is based on the local representation of the solution by the sin-rational fraction. Numerical examples are considered to establish the theoretical development of the method and illustrate the computational accuracy and efficiency.

**Keywords:** Initial value problems, single-step method, rational method, second order method, sin-rational method

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