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

Implicit Two Step Adam Moulton Hybrid Block Method with Two Off-Step Points for Solving Stiff Ordinary Differential Equations

A two step block hybrid Adam Moulton method of uniform order five is presented for the solution of stiff initial value problems. The individual schemes that made up the block method are obtained from the same continuous scheme which is applied to provide the solutions of stiff initial value problems on non overlapping intervals. The constructed block method is consistent, zero – stable and A – stable. Numerical results obtained using the new block method show that it is superior for stiff systems and competes well with existing ones. Keywords: stiff ODEs, Block Method, Adam Moulton method, Stabilit

Order Ten Implicit One-Step Hybrid Block Method for The Solution of Stiff Second-order Ordinary Differential Equations

A one-step hybrid block method for initial value problems of general second order Ordinary Differential Equations has been studied in this paper. The method is developed using interpolation and collocation techniques. The use of the power series approximate solution as an interpolation polynomial and its second derivative as a collocation equation is considered in deriving the method. Numerical analysis shows that the developed new method is consistent, convergent,nbspnbsp and order ten. The new method is then applied to solve the system of second-order ordinary differential equations and the accuracy is better when compared with the existing methods in terms of error

The Direct Simulation of Third Order Linear Problems on Single Step Block Method

In this article, the direct simulation of third order linear problems on single step block method has been proposed. In order to overcoming the setbacks in reduction method, direct method has been proposed using power series to reduce computational burden that occur in the reduction method. Numerical properties for the block method are established and the method developed is consistent, convergent and zero-stable. To validate the accuracy of the block method, certain numerical test problems were considered, the results shown that the accuracy of our method are more accurate over the existing method in literature