Small Modification on Modified Euler Method for Solving Initial Value Problems

Abstract

In this article, small modification to the Modified Euler Method is proposed. Stability and consistency were tested to determine the end result, and some numerical results were presented, and the CPU time was compared again, and it is recognized that the proposed method is more reliable and compatible with higher efficiency.

New Algorithms for Dealing with Fractional Initial Value Problems

“…These methods have confirmed their reliability and validity in dealing with the classical form of problems (1) and (2). In particular, it was declared in [18] that the numerical method that could be used to solve the classical form of problems (1) and (2) applies to the following formulas:…”

“…With the aim of handling the classical version of problems ( 1) and ( 2), two small modifications to the classical Euler Method were proposed in [18]. These methods have confirmed their reliability and validity in dealing with the classical form of problems (1) and (2).…”

Accuracy Improvement of Block Backward Differentiation Formulas for Solving Stiff Ordinary Differential Equations Using Modified Versions of Euler's Method

“…The BBDF-NEM takes less time than BBDF-IMEM and BBDF-MEM. This can be justified by the fact that the NEM is the fastest method to perform functions evaluation followed by MEM and IMEM [26].…”

“…Generally, the MEM is more accurate than Euler's method. Recently, a new version of Euler's method (NEM) with small modification to the MEM was proposed by [12]:…”

“…No detailed study of the implementation of modified versions of Euler's method as starting methods for BBDF has been done yet. It is sufficient to apply the methods proposed by [26] and [22] as to enhance the accuracy of BBDF in terms of absolute error, maximum error and average error.…”