Solution of Higher-Order ODEs Using Backward Difference Method

الملخص EN

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.