Treatment of Lane-Emden Type Equations via Second Derivative Backward Differentiation Formula using Boundary Value Technique
نویسندگان
چکیده
In this paper, second order non-linear ordinary differential equations of Lane-Emden type are solved using the boundary value technique. A class of second derivative backward differentiation formula is derived from some continuous multistep schemes using the multistep collocation technique. The technique transforms the numerical methods to a system of non-linear equations represented as a tridiagonal matrix, thereby obtaining numerical solutions concurrently on the the entire range of integration. General properties of the numerical method are presented as well as the stability properties. Some equations of Lane-Emden type are solved to demonstrate the efficiency of the method.
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