ANALYTICAL SOLUTION OF ORDER 15 AND ORDER 7 FOR INITIAL VALUE PROBLEMS INVOLVING RATIONAL INTEGRATOR

This paper isbasedon a class of rational integrator to establish the region of absolute stability of an order 15 and 7 rational integration, both integrators are constructed from 𝑠(ℎ ̅) = 𝐹(𝑅,𝜃) where F(R,θ) is a complex function. The rational integrating function (RIF) was expanded successfully using polar analysis. The Jordan curve is constructed with the help of MATLAB packages.Furthermore, it was discovered that the rational instability(RIS) are on the positive side of the complex planes of both integrators, while the region of absolute stability was outside the curve. Finally, it was further established that rational integrators fall within the interval 61.48147892 <𝜏 < 61.48148092 and -19.2 < τ< 19.2 where 𝜏 is the encroachment point. It can be said therefore, that both rational integrators formulaare A –stable.