Block Backward Differentiation Formula Method for Solving Van der Pol Equation

The Van der Pol equation is often used as a basic model for oscillatory systems in physics and biology, such as the interaction of two plates on geological faults as well as oscillations in various electrical and electronic systems. The Van der Pol equation is a second-order nonlinear differential equation known to have stiffness properties, especially for large values of the μ parameter. This study aims to develop the Block Backward Differentiation Formula method that is applied in a block manner to solve the Van der Pol equation that is reduced to a system of first-order differential equations. This method is proven to be effective for solving Van der Pol equation with various values of μ parameter, although it requires a fairly small step size to achieve convergence at larger values of μ parameter. The resulting solutions are close to the results provided by Matlab solvers, namely ODE45 and ODE15s