Title: Numerical solutions of initial value problem by using modified Euler's method and Taylor's method

Authors: Rashmi Kumari; V.K. Pandey

Addresses: Department of Mathematics, Radha Govind University, Jharkhand, India ' Department of Mathematics, Radha Govind University, Jharkhand, India

Abstract: The numerical solution of differential equations (DEs) holds paramount importance in mathematical modelling for applications in science and engineering. It is frequently challenging to find accurate solutions to differential equations that define real-life issues due to their complexity. Since analytical solutions are unavailable for most differential equations, the main way to gain meaningful insights into the solution is through numerical computations. This article describes the numerical solutions of fractional differential equations (FDEs) with initial value problem (IVP) using the modified Euler's method (MEM) and Taylor's method (TM). In addition to calculating the precise analytical solution, we also found the solutions to a few numerical problems. Next, for validation, a list of the accuracy discrepancies between analytical and approximation answers is provided. We found that the accuracy of a solution increases with minimal step sizes. Numerical models and figures are shown and analysed to illustrate the efficacy of the proposed methodology.

Keywords: initial value problem; IVP; Taylor's method; modified Euler's method; MEM; numerical solution.

DOI: 10.1504/IJMOR.2026.153578

International Journal of Mathematics in Operational Research, 2026 Vol.34 No.1, pp.100 - 118

Received: 08 Dec 2023
Accepted: 24 Dec 2023
Published online: 18 May 2026 *

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