Abstract
<title>Abstract</title> <p>This study presents a one-sixth multiderivative Chebyshev Imposed Negative-Steps Numerical Method for directly Solving Second-Order ODEs of Order 8 that incorporates negative steps strategy to en hance accuracy and stability when solving linear and nonlinear initial value problems. The derivation uses the techniques of multistep collocation and interpolation, using Chebyshev polynomial of first kind as the basis function for the approximate solution. Within a one-Sixth block, six intrastep points are considered. The values of the unknown parameters were obtained using the Gaussian elimina tion method,which were substituted into the approximate solution to get the continuous scheme and evaluated at the selected point to give the discrete scheme. The order, error constant, accuracy, con sistency, and stability properties of the method are Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method. The results are evaluated against other methods from the literature.</p>