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

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

Four Steps Implicit Method for the Solution of General Second Order Ordinary Differential Equations

Four steps implicit scheme for the solution of second order ordinary differential equation was derived through interpolation and collocation method. Newton polynomial approximation method was used to generate the unknown parameters in the corrector. The method was tested with numerical examples and it was found to be efficient in solving second order ordinary differential equations

Solving General Second Order Ordinary Differential Equations by a One-Step Hybrid Collocation Method

A one-step hybrid method is developed for the numerical approximation of second order initial value problems of ordinary differential equations by interpolation and collocation at nonstop and step points respectively. The method is zero stable and consistent with very small error term. Numerical experiment of the method on sample problem shows that the method is more efficient and accurate than the results obtained from our earlier methods

Continuous Implicit method for the Solution of General Second Order Ordinary Differential Equations

Abstract Methods of collocation and interpolation were adopted to generate a continuous implicit scheme for the solution of second order ordinary differential equation. Newton polynomial approximation method was used to generate the unknown parameter in the corrector. This enables us to solve both initial and boundary value problems

Three Steps Hybrid Block Method for the Solution of General Second Order Ordinary Differential Equations

Block method is adopted in this paper for the direct solution of second order ordinary differential equations. The method is derived by collocation and interpolation of power series approximate solution to give a continuous hybrid linear multistep method which is implemented in block method to derive the independent solution at selected grid points. The properties of the derived scheme were investigated and found to be zero-stable, consistent and convergent. The efficiency of the derived method was tested and found to compare favourably with the existing methods

One-Step Implicit Hybrid Block Method for The Direct Solution of General Second Order Ordinary Differential Equations

A one-step implicit hybrid block solution method for initial value problems of general second order ordinary differential equations has been studied in this paper. The onestep method is augmented by the inclusion of off step points to enable the multistep procedure. This guaranteed zero stability as well as consistency of the resulting method. The convergence and weak stability properties of the new method have been established. Results from the new method compared with those obtained from existing methods show that the new method gives better accuracy

Numerov's Method for the Solution of Second Order Initial Value Problems of Ordinary Differential Equation Using Modified Block Method

Collocation and interpolation method us;ng power series approximate solution to generate a continuous Numerov's is considered in this paper. The existing block method was modified to accommodate the unknown parameter in the corrector. The modified block method generates the independent solution at the grid points. This method was found to be efficient when tested on second order ordinary differential equation. Keywords: Collocation, interpolation, approximate solution, block method, grid poin

An A(α)-Stable Method for Solving Initial Value Problems of Ordinary Differential Equations

An A(α)-stable implicit one step hybrid method for the numerical approximation of solutions of initial value problems of general second order ordinary differential equations is proposed. The method is developed by interpolation and collocation of a power series approximate solution and implemented as simultaneous integrators via block method. The stability and convergence of the methods are determined. Numerical experiments are conducted on sample problems and the absolute error estimates of the results are presented