On Euler’s And Milne’s Linear Multi Step Methods of Solving the Ordinary Differential Equations [2010MSC: 65XX] | Asian Journal of Pure and Applied Mathematics

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.

 

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Keywords: Continuous functions, ordinary differential equations iterations, integral equations, initial value problems, convergence