The direct solution of general second order ordinary differential equation 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 modified block is adopted to generate the independent solution at the grid points. This method was found to be efficient when tested on second order ordinary differential equation

/pdf/a-modified-block-method-for-the-direct-solution-of-second-scnipv6nw4.pdf

A modified block method for the direct solution of second order ordinary differential equations

We proposed a continuous blocks method for the solution of second order initial value problems with constant step size in this paper. The method was developed by interpolation and collocation of power series approximate solution to generate a continuous linear multistep method;this is evaluated for the independent solution to give a continuous block method which is evaluated at selected grid point to give discrete block method. The basic properties of the method were investigated and was found to be zero stable, consistent and convergent. The efficiency of the method was tested on somenumerical examples and found to give better approximation than the existing methods.

/pdf/continuous-block-method-for-the-solution-of-second-order-1pri0zzkpy.pdf

Continuous block method for the solution of second order initial value problems of ordinary differential equation

This paper aims to provide a direct solution to third order initial value problems of ordinary differential equations. Multistep collocation approach is adopted in the derivation of the method. The new block method is zero-stable, consistent and convergent. The application of the new method to solving differential equations gives better results when compared with the existing methods.

/pdf/numerical-solution-of-third-order-ordinary-differential-3xw2ftlwlv.pdf

Numerical solution of third order ordinary differential equations using a seven-step block method

The paper presents a one step hybrid numerical scheme with two off grid points for solving directly the general second order initial value problems of ordinary differential equations. The scheme is developed using collocation and interpolation technique. The proposed scheme is consistent, zero stable and of order four. This scheme can estimate the approximate solution at both step and off step points simultaneously by using variable step size. Numerical results are given to show the efficiency of the proposed scheme over the existing schemes.

/pdf/an-efficient-hybrid-numerical-scheme-for-solvinggeneral-2uuatrbcax.pdf

An efficient hybrid numerical scheme for solvinggeneral second order initial value problems (IVPs)

This article presented the direct block predictor-corrector method for solving general higher order initial value problems of ordinary differential equation. Method of collocation and interpolation of power series approximate solution was used to derive a continuous linear multistep method. Block method was later used to generate the non overlapping solution at selected grid points. The method developed, is self starting, consistent, symmetric, zero-stable and convergent. The performance of the new block method was tested with some fourth order initial value problems and it was found to compare favorably with the existing methods.

/pdf/direct-block-predictor-corrector-method-for-the-solution-of-2a512fu3ib.pdf

Direct Block Predictor-Corrector Method for the Solution of General Fourth Order Odes

A block linear multistep method for solving special third order initial value problems of ordinary differential equations is presented in this paper. The approach of collocation approximation is adopted in the derivation of the scheme and then the scheme is applied as simultaneous integrator to special third order initial value problem of ordinary differential equations. This implementation strategy is more accurate and efficient than those given when the same scheme is applied over overlapping intervals in predictor-corrector mode. Furthermore, the new block method possesses the desirable feature of Runge-Kutta method of being self-starting and eliminates the use of predictor- corrector method. Experimental results confirm the superiority of the new scheme over the existing methods.

http://www.akamaiuniversity.us/PJST10_1_136.pdf

BT Olabode

Papers

An accurate scheme by block method for third order ordinary differential equations