Solution of Higher‐Order ODEs Using Backward Difference Method

The current numerical technique for solving a system of higher‐order ordinary differential equations (ODEs) is to reduce it to a system of first‐order equations then solving it using first‐order ODE methods. Here, we propose a method to solve higher‐order ODEs directly. The formulae will be derived in terms of backward difference in a constant stepsize formulation. The method developed will be validated by solving some higher‐order ODEs directly with constant stepsize. To simplify the evaluations of the integration coefficients, we find the relationship between various orders. The result presented confirmed our hypothesis.