On Euler’s And Milne’s Linear Multi Step Methods of Solving the Ordinary Differential Equations [201

This work discusses the Euler’s and Milne’s linear multistep methods for solving initial value problems of the ordinary differential equations. By this for the Euler’s we seek an approximation Capture_1.PNG Capture_3.PNG and for the integral equation Capture-_7.PNG with a truncation errorCapture_-_5.PNG . Thereby providing an enhancement accuracy and for the Milne’s method for the integral equationCapture_21.PNG the iterative formula: Capture-_8.PNGConverges faster where the local truncation error Capture_-_9.PNG is sufficiently negligible compared to that of Euler. Hence, the milne’ method is a more accurate approximation method than the Euler’s method. Section three points to the fact that linear multi step method so far discussed is convergent provided it is consistent and stable. This result is achievable if the root conditions are satisfied.

Please read full article –https://www.globalpresshub.com/index.php/AJPAM/