An Application of Second Derivative Backward Differentiation Formula Hybrid Block Method on Stiff Ordinary Differential Equations

In this paper, we developed a continuous scheme of four and five step with one off-grid point at collocation which provides the approximate solution of both linear and nonlinear stiff ordinary differential equations with constant step size. The continuous scheme is evaluated at both interpolation and collocation where necessary to give continuous hybrid block scheme and high order of accuracy with low error constants. Numerical results of the schemes are presented to compare with exact solutions and the results have shown that the (SDHBBDF) performed favorably when compare with existing methods. Keywords: Collocation and interpolation, Hybrid block methods, Second Derivative and Stiff system

On some properties of the block linear multi-step methods

The convergence, stability and order of Block linear Multistep methods have been determined in the past based on individual members of the block. In this paper, methods are proposed to examine the properties of the entire block. Some Block Linear Multistep methods have been considered, their convergence, stability and order have been determined using these approaches. Keywords: Annuity, Amortisation, Sinking Fund, Present and Future Value Annuity, Maturity date and Redemption value

A Class of A-Stable Order Four and Six Linear Multistep Methods for Stiff Initial Value Problems

A new three and five step block linear methods based on the Adams family for the direct solution of stiff initial value problems (IVPs) are proposed. The main methods together with the additional methods which constitute the block methods are derived via interpolation and collocation procedures. These methods are of uniform order four and six for the three and five step methods respectively. The stability analysis of the two methods indicates that the methods are A–stable, consistent and zero stable. Numerical results obtained using the proposed new block methods show that they are attractive for the solutions of stiff problems and compete favorably with the well-known Matlab stiff ODE solver ODE23S. Keywords: Linear multistep methods, initial value problems, interpolation and collocation