Block hybrid method with off-step points for numerical solutions of classical Blasius Equation in fluid dynamics

Changes in conditions and parameters of equations in fluid dynamics can place a significant burden on procedures that lead to their approximate analytic solutions. While some classes of numerical methods can easily accommodate such changes, explicit linear multistep methods (LMM) have problems of instability. In this research – in order to address problem of instability associated with explicit LMM when used to solve nonlinear differential equations – a hybrid form of explicit LMM incorporating two off-step points in block form was derived using multistep collocation and matrix inversion technique. The two off-step points involved an interpolation point and a collocation point. Furthermore, the derived block method was shown to be convergent; investigation of its region of absolute stability indicated an A(\alpha )-stable method having large region of absolute stability with \alpha=۸۸.۷^{۰} and capable of handling nonlinear systems. For implementation purpose, it was tested on classical Blasius problem in fluid dynamics and results compared well with Matlab ode۲۳s known for solving stiff and nonlinear problems.

کلیدواژه ها:

Approximate ، collocation ، Interpolation ، Multistep ، block