Variable order step size algorithm for solving second order ODEs

Previous multi step method using a divided difference formulation for solving higher order ordinary differential equations (ODEs) requires calculating the integration co-efficients at every step. In the current research, a multi step method in backwards difference form is established. The backward difference formulation offers a solution to the tedious calculation of integration coefficients. Rather than calculating inte-gration coefficients at every step change, a backward difference formulation requires calculating integration coefficients only once in the beginning and if required once more at the end. The proposed method will also be equipped with a variable order step size algorithm to reduce computational cost (calculation time). Both linear and nonlinear second order ODEs will used to validate the accuracy and efficiency of the proposed method.

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