Numerical Approximation for Direct Solution of Third-Order Ordinary Differential Equations Using New Class of Falkner-Type Block Method

Abstract

In this article, a new class of Falkner-type methods for direct solution of third order ordinary differential equation is developed. The approach of collocation and interpolation technique is adopted to derive the new Falkner-type methods, which is implemented in block mode to get approximation at grids points simultaneously. The resulting scheme is zero-stable, consistent and convergent with good region of absolute stability. The tabular and graphical presentations of the numerical results to the problems considered, demonstrate the effectiveness and good accuracy of the scheme in comparison with other methods