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method is presented in this paper which employs cubic B-spline to solve two point second order boundary value problems for ordinary differential equations. First, heat problem is modeled as second order boundary value problem. Then, B-spline method for both linear and non-linear cases is discussed. Selected numerical examples for both the cases are solved using MATLAB, which demonstrate the applicability and efficiency of present method. To be more accessible for practicing engineers and applied mathematicians there is a need for methods, which are easy and ready for computer implementation. The B-spline techniques appear to be an ideal tool to attain these goals. An added advantage of present method is that it does not require modification while switching from linear to non-linear problem.

A Numerical Algorithm for Solution of Boundary Value Problems with Applications