Modified Block Method for the Direct Solution of Second Order Ordinary Differential Equations

The direct solution of general second order ordinary differential equations is considered in this paper. The method is based on the collocation and interpolation of the power series approximate solution to generate a continuous linear multistep method. We modified the existing block method in order to accommodate the general nth order ordinary differential equation. The method was found to be efficient when tested on second order ordinary differential equation

Two Steps Block Method for the Solution of General Second Order Initial Value Problems of Ordinary Differential Equation

In this paper, an implicit block linear multistep method for the solution of ordinary differential equation was extended to the general form of differential equation. This method is self starting and does not need a predictor to solve for the unknown in the corrector. The method can also be extended to boundary value problems without additional cost. The method was found to be efficient after being tested with numerical problems of second order

A One Step Method for the Solution of General Second Order Ordinary Differential Equations

In this paper, an implicit one step method for the numerical solution of second order initial value problems of ordinary differential equations has been developed by collocation and interpolation technique. The introduction of an o step point guaranteed the zero stability and consistency of the method. The implicit method developed was implemented as a block which gave simultaneous solutions, as well as their rst derivatives, at both o step and the step point. A comparison of our method to the predictor-corrector method after solving some sample problems reveals that our method performs better

Block Algorithm for General Third Order Ordinary Differential Equation

We present a block algorithm for the general solution o

Development of Hybrid Block Integrator for the Numerical solution of Stiff and Oscillatory Differential Equations for first order Ordinary Differential Equations

This paper discussed the development of a new numerical hybrid block integrator for the numerical solution of stiff and oscillatory differential equations for first order ordinary differential equations. The method of interpolation and collocation at some selected grid point to generate the continuous scheme was adopted. The research also investigates the consistency, convergence, zero-stability and region of absolute stability of the integrator using matlab and the integrator was tested on some numerical experiments for comparism. The analysis of the method showed that the method is Zero-stable, consistent, convergent and computationally stable. The method handles stiff and Oscillatory differential equations effectively. AMS Subject Classification: 65L05, 65L06, 65D3

Starting Order Seven Method Accurately for the Solution of First Initial Value Problems of First Order Ordinary Differential Equations

In this paper, we developed an order seven linear multistep method, which is implemented in predictor corrector-method. The corrector is developed by method of collocation and interpolation of power series, approximate solutions at some selected grid points, to give a continuous linear multistep method, which is evaluated at some selected grid points to give a discrete linear multistep method of order seven. The predictors were also developed by method of collocation and interpolation of power series approximate solution, to give a continuous linear multistep method. The continuous linear multistep method is then solved for the independent solution to give a continuous block formula, which is evaluated at some selected grid points to give discrete block method. Basic properties of the corrector was investigated and found to be zero stable, consistent and convergent. The efficiency of the method was tested on some numerical experiments and found to compare favorably with the existing methods