Volume : 6, Issue : 4, April - 2017

An Analysis of Numerical Solutions and Errors with Euler�s Method

Parvesh Ranga

Abstract :

<p>&nbsp;<b><i><span style="font-size:11.0pt;line-height:115%;&#10;font-family:&quot;Calii&quot;,sans-serif;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:&#10;Calii;mso-fareast-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;&#10;mso-bidi-font-family:Mangal;mso-bidi-theme-font:minor-bidi;mso-ansi-language:&#10;EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA">This paper mainly presents Euler method for solving initial value problems (IVP) for ordinary differential equations (ODE). The proposed method is efficient and practically well suited for solving these problems. In order to verify the accuracy, we compare numerical solutions with the exact solutions. The numerical solutions are in good agreement with the exact solutions.&nbsp; In order to achieve higher accuracy in the solution, the step size needs to be very small. Finally we investigate and compute the errors of the euler&rsquo;s method for different step sizes&nbsp;</span></i></b></p>