Numerical integration of stiff problems using a new time-efficient hybrid block solver based on collocation and interpolation techniques

Abstract

In this study, an optimal L-stable time-efficient hybrid block method with a relative measure of stability is developed for solving stiff systems in ordinary differential equations. The derivation resorts to interpolation and collocation techniques over a single step with two intermediate points, resulting in an efficient one-step method. The optimization of the two off-grid points is achieved by means of the local truncation error (LTE) of the main formula. The theoretical analysis shows that the method is consistent, zero-stable, seventh-order convergent for the main formula, and L-stable. The highly stiff systems solved with the proposed and other algorithms (even of higher-order than the proposed one) proved the efficiency of the former in the context of several types of errors, precision factors, and computational time.