Variable step three-point block methods for solving stiff ordinary differential equations

In this paper, we consider the numerical solution of first order stiff ordinary differential equations (ODEs) by a class of variable step size three points Block Backward Differentiation Formulas (BBDFs) methods. The basic formulation using three back values and the step size controlling strategy is described. In order to optimize the performance in terms of precision and the computational time, all the coefficients of the method will be stored in simplified form to avoid the repetitive computation of the coefficients as the step changes in the integration interval. Numerical results show the 3-point BBDF method gives better accuracy compared to the existing ODE solver, ode15s when solving ODEs problems