Numerical Integration of Fourth-Order Initial Value Problems of Odes Using a Seventh-Order Linear Multistep Scheme

This paper introduces a seventh-order linear multistep method for the numerical integration of fourth-order initial value problems. The method is derived by constructing a continuous scheme by carefully applying collocation and interpolation to the Chebyshev polynomial at chosen points, and evaluating it at a specific grid point. The stability of the method is analyzed, and its convergence is proven. Numerical examples are provided to demonstrate the accuracy and efficiency of the proposed method compared to existing methods. The results show that the new method is a viable alternative for solving fourth-order initial value problems.