A Numerical Solutions Of Initial Value Problems (Ivp) For Ordinary Differential Equations (Ode) With Euler And Higher Order Of Runge Kutta Methods Using Matlab
Journal Title: International Journal of Engineering and Science Invention - Year 2018, Vol 7, Issue 4
Abstract
This Paper Mainly Presents Euler Method And 4 thorder Runge Kutta Method (RK4) For Solving Initial Value Problems (IVP) For Ordinary Differential Equations (ODE). The Two Proposed Methods Are Quite 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. Numerical Comparisons Between Euler Method And Runge Kutta Method Have Been Presented Using Matlab. Also We Compare The Performance And The Computational Effort Of Such Methods. 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 Two Proposed Methods For Different Step Sizes To Examine Superiority. Several Numerical Examples Are Given.
Authors and Affiliations
C. Senthilnathan
Keywords
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