We consider developing a four-step one offgrid block hybrid method for the solution of fourth derivative Ordinary Differential Equations. Method of interpolation and collocation of power series approximate solution was used as the basis function to generate the continuous hybrid linear multistep method, which was then evaluated at non-interpolating points to give a continuous block method. The discrete block method was recovered when the continuous block was evaluated at all step points. The basic properties of the methods were investigated and said to be converge. The developed four-step method is applied to solve fourth derivative problems of ordinary differential equations from the numerical results obtained; it is observed that the developed method gives better approximation than the existing method compared with.
An optimized half-step third derivative block scheme on testing third order initial value problems is presented in this article. This scheme suggests some certain points of evaluation which properly optimizes the truncation errors at point of formulas, the conditions that guarantee the properties of the method was considered and satisfied. However the develop scheme is used to test some third order optimized problems and the mathematical outcomes achieved confirms better calculation than the previous method we related with.
In this paper a three-step two hybrid block method with two offgrid hybrid points chosen within interval [Xn,Xn+1] and [Xn+1,Xn+2] was developed to solve second Order Ordinary Differential Equations directly, using the power series as the basic function to approximate and generate some continuous schemes. The basic properties of the method was investigated and was found to converge. Numerical Solution of our method was tested on some stiff equations and was found to give better approximation than the existing method.
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