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A different amalgamation of non-polynomial splines is used to find the approximate solution of linear and non-linear second order boundary value problems.Cubic spline functions are assembled with exponential and trigonometric functions to develop the different orders of numerical schemes. Free parameter k of the non-polynomial part is also used to form a new scheme, which elevates the accuracy of the solution. Numerical illustrations are given to validate the applicability and feasibility of the present method and also depicted in the graphs.

A smooth approximation for non-linear second order boundary value problems using composite non-polynomial spline functions