On the Numerical Approximation of First-order Riccati Differential Equations by Two-step Second Derivative Block Method with Bernstein Polynomial Basis

A new two-step second derivative block method (TSDBM) using Bernstein polynomial of convergence order six for solving Riccati Differential Equations (RDEs) is presented. The TSDBM is constructed on collocation and interpolation procedures at the specific points and executed as block mode in other to calculate the approximate solution at two-point per phase with less computation time in seconds. The method was investigated for the basic properties and established to be zero stable, and convergent. The TSDBM was applied to six test problems varying from nonlinear, and exponential RDEs. The numerical results of TSDBM were displayed in the tables and the TSDBM shows competence over some existing methods in the literature. The absolute error of the TSDBM and the time taken for the computation were also examined and presented in tables for more clarifications.