A Family of Fifth Order A (α)-Stable Numerical Integrators for the Solution of y''' = f(х, y', y'', y''')

Abstract

In this paper, fifth order A(α)-stable numerical integrators for the direct solution to third order ordinary differential equations are proposed. Collocation and interpolation approach were adopted to generate continuous hybrid multistep methods. The use of power series as a basis function was adopted for approximate solution. Evaluation was done at off-grid points to get continuous hybrid multistep methods. Block method was later adopted to generate the independent solution at selected off-grid points. The properties of the block viz: order, zero stability and region of absolute stability are investigated. The proposed methods were tested on third order ordinary differential equations and found to give better result when compared with existing methods.